here at verse 23 chapter 2, I'll read to verse 28, we'll get into our study. And what we're looking at today is Jesus who is the Lord of the Sabbath. So beginning at verse 23 it happened that he went through the grain fields on the Sabbath and as they went, his disciples began to pluck the heads of grain. The Pharisees said to him, look, why do they do what is not lawful on the Sabbath? But he said to them, have you never read what David did when he was in need and hungry? He and those with him, how he went into the house of God in the days of Abba Arthur, the high priest and ate the showbread, which is not lawful to eat except for the priests and also gave some to those who are with him. He said to them, the Sabbath was made for man and not man for the Sabbath. Therefore, the Son of Man is also Lord of the Sabbath. So as we've been going through the Gospel of Mark, we've seen that Jesus is presently growing in fame. He's become very popular and many are beginning to follow him and many are listening to him. When Jesus was in a synagogue, he had cast a demon out of a man and the Bible tells us that when he did that the people were amazed and they had said, what is this? What new doctrine is this? Even demons obey him. The result we see in Mark 1.28 says immediately his fame spread throughout all the region around Galilee. After Jesus had healed Peter's mother-in-law, great amounts of people began to come to him. Mark 1.33 says the whole city was gathered together at the door of Peter's house. Later we saw how that Peter had told Jesus, everyone is looking for you and they were. Shortly thereafter, Jesus cleansed the leper, told him not to say anything but he disobeyed and the result was Jesus could no longer enter the city. That all happened in chapter 1. Chapter 2 continued in the same way. Jesus returned to the city of Capernaum. People heard that he was in Peter's home and the result was a crowd came and there was no room to receive them. Jesus revealed that he not only healed but he also cast out demons and forgave sins and as a result, as we've seen, religious opposition began to grow opposing him. So at this point, religious leaders are now unifying in rejection of Jesus Christ and his message. Now they have accused him of blasphemy and they did so because he had forgiven the paralytic of his sins. Remember in Mark chapter 2 verse 7 how they said, why does this man speak blasphemies like this? Who can forgive sins but God alone? And then also they inferred that he was guilty of living an unholy life. You saw that in Mark 2 verse 16 where they said, how is it that he eats and drinks with tax collectors and sinners? So today we're going to look at controversies that relate to the observation of the Sabbath. Verses 23, 3, 28 relate to physical labor being performed on the Sabbath and then in chapter 3 verses 1 through 5, those verses center on Jesus healing a crippled man again on the Sabbath. So let me lay a context so that you can understand what's taking place here in these two studies we're going to have because in reality these actually could be two separate studies that I'm combining into one. To understand I need to take a moment to develop what would be called a very basic concept of Shabbat or the Sabbath. Shabbat literally speaks of the ceasing of work. It speaks of inactivity or resting. All the way in the book of Genesis in chapter 2 verse 3 it says that God blessed the seventh day and sanctified it because in it he rested from all his work which God had created and made. So from the beginning the Lord declared the Sabbath to be a time of rest. It was a time of remembrance. When God gave the law of Moses God commanded the Jews to observe the Sabbath. In the book of Exodus chapter 20 verses 9 through 11 it says six days shall you labor and do all your work but the seventh day is the Sabbath of the Lord your God. In it you shall do no work. You nor your son nor your daughter your man's servant nor your maid's servant nor your cattle nor your stranger that's within your gates for in six days the Lord made heaven and earth the sea and all that is in them and rested the seventh day wherefore the Lord blessed the Sabbath day and hollowed it or sanctified set it apart. So it was set apart for the Jews in order that they would remember him on that day. Now I want you to know this and I'm going to develop a thought about this. It was a day that was set apart for Israel to reverence God and to rest from labor. It was intended to promote worship of God which produced love for God and love for others because when you love God the fruit is going to be that you love other people and that by the way is how we can know that we are Christians. In 1 John chapter 4 verse 20 and 21 it says if someone says I love God and hates his brother he's a liar for he who does not love his brother whom he has seen how can he love God whom he has not seen. This commandment we have from him that he who loves God must love his brother also. So the Sabbath was intended to promote worship of God and the worship of God love is going to be for God but it's going to be also given to other people. It's going to be something that that reflects the reality that you know the Lord and so the Sabbath rest was intended to give people an opportunity to worship God and the fruit of such worship would be loving him and loving others and that is the purpose of gathering together in what we today call worship services. Worship services are intended to glorify God and unify people in the worship of him and any service that does not promote worship and spiritual unity is just a meeting. Over the centuries the Jewish religious leaders had observed the Sabbath that was in keeping with the commands that God had given to Israel and over time they had added their traditions to God's commandments concerning it. All in any kind of work imaginable became strictly forbidden. There's a book that I have it's called The Life and Times of Jesus the Messiah it's written by a messianic Jewish man by the name of Alfred Adarshim and he wrote tailors didn't carry a needle for fear they might be tempted to sew. Clothing could not be washed or dyed fires could not be lit or extinguished baths could not be taken for fear water would fall on the floor and wash it you could not carry anything heavier than a dried fig chairs could not be moved because dragon them might make a furrow in the ground women didn't look into mirrors in the event that they might see a gray hair and pluck it out no that's not true they'd never do that false teeth could not be worn because they exceeded the weight limit that you were allowed to carry think about that one sick people were only allowed enough treatment to keep them alive because any treatment that could improve their condition was work so the result was the Sabbath became a time of frustration and stress the people became tired of bearing a yoke of man-made oppressive regulations because the Sabbath became a burden a burden that was placed on them because of the Pharisees the Sabbath now one final word I added this because I've been asked this and I thought well it'd be worth taking just a moment to to say something about we've been asked why we worship on Sunday and not Saturday I remember years ago now many years ago doing a doing a Sunday morning service I was that's when we're in the chapel before we built this sanctuary and a lady walked up to me after the service and said to me this is my first time here and the Lord has placed something on my heart to tell you I said okay she says this is from the Lord I said well let's hear what he has to say I'm used to hearing that from Marie but if you want to say it okay she said the Lord is doing a good work here but God says that you need to meet on the Sabbath Saturday and he'll do a greater work and I said no he didn't he didn't say that I said you're saying that it's because the Bible doesn't teach that and let me share with you what the Bible says basically about this okay why do we worship on Sunday and not Saturday well the brief answer is that the law of the Sabbath is not for the church the law of the Sabbath is for Israel how do we know that well Exodus chapter 31 verse 13 speak also to the children of Israel saying surely my Sabbaths you shall keep for it is a sign between me and you throughout your generations that you may know that I am the Lord who sanctifies you the Sabbath meeting on the Saturday is actually a covenant relationship that God has with the children of Israel and not the church the church observes Sunday as the day of rest because Jesus was resurrected on Sunday and it was very early the practice of the early church in 1st Corinthians 16 verse 2 on the first day of the week each one of you should set aside a sum of money and keeping with your income saving it up so that when I come no collections will have to be made on the first day of the week and that first day of the week became known as the Lord's day in Revelation chapter 1 verse 10 I was in the spirit on the Lord's day and I heard behind me a loud voice as of a trumpet so Christians observe a day of rest and attend services because we've been saved and the early church met on the first day of the week for God's word and for worship we met on the first day of the week because that's the day Christ was resurrected and when the church would gather there was a purpose it says in Acts 242 that the church devoted themselves to the apostles teaching and fellowship to the breaking of bread and to prayer and so when the church gathers together the church is intended to be taught to love God and love others remember that when when Jesus was approached and asked what is the greatest commandment in the law he said to love the Lord thy God with all your heart so strength in mind he said this is a first and great commandment there's a second like unto it and you shall love your neighbor as yourself upon these two commands hang all the law and the prophets and so when the when the when the people would gather for a rest they actually rested then they began to meet and when they would meet on Shabbat on the Sabbath it was for teaching of the word of God it was for fellowship but it was also to encourage them to love one another see when you transform people from within by the word of God and power of the Spirit and they begin to love one another that's intended to be something God uses to reach a nation it's that's what will change nations and so when we gather together on a Sunday or a Wednesday we gather together so that we might together get into the word of God and worship him so that when we walk out of this this place here on Sunday or Wednesday or whenever we gather our lives are being changed because the way that this nation is going to be changed is one person at a time and I think that what we've done today and I'll say this quickly is that we have forgotten that and the church by and large seeing the danger has gotten caught up so much with the danger that they're forgetting to feed the sheep and it's the sheep that are going to go out and deal with the danger years ago some of you might remember something was called Y2K you guys remember that yeah I used to say it do okay but Y2K I'm sorry that's an old one that's an obviously old Y2K and we were being told that all of the you know everything was going to change because computers and things are going to fail and this and that and so the church began to run around like chicken little saying that the sky is falling and the church has the tendency of doing that we get caught up with the moment and then somehow we're going to fix it they're doing certain things which I think we have to be careful that we don't get caught up so much in the fixing of things because we're afraid of what's going on and forget that the primary cause that we have been created to do or for is to reach people with the gospel of Jesus Christ because indeed if things are going down and in many ways we see that they do and continue to do so and historically have then what we ought to be caring about is their souls because where are they going to end up where's their faith what's going to happen to them and so for me the primary thing has always been teaching the word of God yes we see the things that are going on yes we ought to be taking care of these things yes we ought to be involved in whatever way that we may and the Holy Spirit leads us to yes we should be voting yes we should be telling our friends you know to be aware of the times yes all of that is a yes with me but the number one thing is the gospel of Jesus Christ because that's what changes people's lives and that's what we have to understand and so when we gather on a Sunday morning it isn't so that I can give you an update and all the things that are going on in the world because you have the ability to see yourself what I'm supposed to do as a pastor teacher is to teach the word of God because God gave some to be apostles, prophets, evangelists, pastors and teachers for the equipping of the saints for the work of ministry and so as we gather together and worship God we'll love one another love other people and we can transform a nation and that's how it works and when the church would gather or the the Jews during the time of Christ would gather together and they would have their synagogue meetings it was intended that they might learn to love God and love other people that's what it was supposed to do that's what the teaching of the word was intended to equip them to do and so Jesus is there and it's a Sabbath day it's a Shabbat it's a Sabbath day and Jesus is there in the synagogue and what's going to take place now is that the Lord is going to be giving some insight into what he has just been speaking about because he had just spoken concerning new wine he had said in verse 22 of the same chapter he said no one puts new wine into old wineskins or else the new wine bursts the wineskins and the wine is spilled and the wineskins are ruined but new wine must be put into new wineskins he's going to be sharing with him a bit about that and so in verse 23 it says it happened that as he went through the grain fields on the Sabbath it says that they as they went his disciples began to pluck the the heads of grain and so when you cross-reference this with other passages that speak of the same event Matthew chapter 12 verse 1 tells us that his disciples were hungry so they began to pick the grain now immediately you might be thinking well they're stealing aren't they I mean they're going through and they're taking things from the from the fields that don't belong to them but they weren't stealing according to the Old Testament book of Deuteronomy 23 verse 25 it says if you enter your neighbor's grain field you may pick kernels with your hands but you must not put a sickle to their standing grain and so they could go in and they could do this it was within the confines of the law why because they were hungry and they could feed themselves you see to harvest the grain would be stealing but to pluck the grain was allowed to take a few heads of grain as you walked was allowed if you were hungry and this is one of the ways that the Lord provided for the people and that would include him providing for those who were poor in the viticus 19 verse 10 it says you shall not glean your vineyard neither shall you gather every grape of your vineyard you shall leave them for the poor and stranger I am the Lord your God and that was how the Lord would minister to those who were in need somebody didn't go and pick the grain and give it to them those who were hungry went in and on their own they were to pick the grain and feed themselves well as this is taking place the Pharisee see this notice in verse 24 the Pharisee said to him look why do they do what is not lawful on the Sabbath so immediately they bring a question now earlier we saw how the Pharisees had asked the disciples about why Jesus was doing something but now they approach him personally and they want he want they want to know something about what the disciples are doing what they're doing is they're accusing the disciples of threshing grain threshing grain is unlawful on Shabbat in Luke chapter 6 verse 1 it says one Sabbath Jesus was going through the grain fields and his disciples began to pick some heads of grain to rub them in their hands and to eat the kernels so they believed that the rubbing of the grain to remove the husk and shells that was threshing they thought they were reaping they thought they were sifting they thought they were threshing winnowing and they thought they were preparing a meal and this all broke their traditional interpretation of keeping the Sabbath now the law never said that this is the tradition and their tradition was equal to what God's word said the actual charge is simple your disciples have broken our regulations and traditions well Jesus responds in verse 25 he says to them have you never read what David did when he was in need and hungry he and those with him how he went into the house of God in the days of abbey after the high priest and ate the showbread which is not lawful to eat except for the priests and also gave some to those who were with him have you never read now this is very similar to what he had said to uh a little bit earlier he had said uh something similar to the Pharisees when he was eating with with the sinners and in Matthew 9 13 he had said to them go and learn what this means I desire mercy and not sacrifice so when he says have you never read that's a way of saying you know the facts but you don't understand you don't know the meaning you are teachers of others but you haven't learned the lesson yourself you profess to be experts on scripture but you don't understand its meaning so rather than arguing about their religious traditions notice Jesus takes them to the the word of God you see they were using his teachings to bolster their arguments and so Jesus rebukes them and 2 Timothy 3 16 and 17 it says all scripture is God breathe and is useful for teaching for rebuking for correcting and training in righteousness so that the man of God may be thoroughly equipped for every good work and so he refers to the scripture he doesn't just argue with them about their tradition he says have you never read do you not understand and he speaks concerning David now that David was fleeing from King Saul this is found in the Old Testament book of 1st Samuel chapter 21 David and his man had fled to a city it was called the city of knob that's where the tabernacle the temporary dwelling place of the Lord was and David and his men had no food and they were hungry so to feed them he and his men were allowed to eat what is called the show bread the show bread is also referred to in scripture as the bread of the presence these were 12 loaves of bread they were baked weekly and they represented the 12 tribes of Israel in Exodus 29 32 it says at the entrance to the tent of meeting Aaron and his sons are to eat the meat of the ram and the bread that is in the basket they are to eat these offerings by which atonement was made for their ordination and consecration no one else may eat them because they are sacred so the loaves of bread were put in a place called the holy place and they were set on a table they symbolized Israel and its dependence on God to provide for their life and their nourishment and the bread of the presence stood as an act of thanksgiving to God for providing for the nation it was placed on a golden table and the 12 loaves would remain a week and then would be replaced by freshly baked bread and at that time the priests could eat the loaves that had been replaced so Jesus made it clear David and his men were not priests but were allowed to eat the bread and this is because the men were in need and exceptions can be made when somebody is in need notice in verse 27 he said to them the Sabbath was made for men and not man for the Sabbath God allowed the ceremonial law to be violated in order that David and his men might be fed human need is more important than man made traditions therefore verse 28 the son of man is also lord of the Sabbath now when saying this Jesus announced he had authority over the Jewish religion he knew the scriptures and they were arguing with the one who was the center of them it's kind of like if somebody was trying to tell you about you and they didn't know that they were speaking of you say you wrote a book there's no picture of you on the book and they read your book and then they're explaining to you what you wrote and what you meant in that book when you're talking about your life and they're starting to argue with you about it they're saying well you know blah blah blah and you say no that's not no no no you don't know I read the book and the book says this this isn't that but it's about you you're the one who wrote it and it's that's what they're doing Jesus Christ is the inspirer of the scripture and they're trying to argue with the one who gave the word it makes absolutely no sense at all and so when Jesus is speaking to them Jesus is saying something that's very powerful he's saying that he is the lord of the Sabbath he knew the scriptures and they were arguing with the one who's the center room because it's God who gave the commandments and God gave the command about the Sabbath so to to claim to be Lord of the Sabbath is to claim deity is what he was doing and so when he made that statement it was very powerful this phrase the Lord of the Sabbath is to make a claim for deity even as earlier he had forgiven a man of his sins and he was claiming to be God he's doing it again by referring himself to himself as the Lord of the Sabbath and so we pick up in verse one of chapter three and he entered the synagogue again and man was there who had a withered hand so they watched him closely whether he would heal him on the Sabbath so they might accuse him and he said to the man who had the withered hand step forward then he said to them is it lawful on the Sabbath to do good or to do evil to save life or to kill and they kept silent and when he had looked around at them with anger being grieved by the hardness of their hearts he said to the man stretch out your hand and he stretched it out and his hand was restored as whole as the other now Jesus is entering the synagogue it's an unnamed city notice that it's more than likely Capernaum and now he's going to give to us an illustration to the fact that he's the Lord of the Sabbath notice verse one there's a man with a withered hand that word withered speaks of crippled or paralyzed and he's there in the service for some reason Luke wants to make sure that we know in chapter six verse six that it's the man's right hand that is crippled now when it says it is withered withered is a word that actually would be used to speak of atrophy so some scholars say that the word indicates that it was a result of an injury and so there's this man he's in the synagogue service and notice verse two they're watching him closely whether he would heal him on the Sabbath when it says they watched him that word watch means to observe closely with evil intent they're looking for something bad they're watching to see if he actually does something good on the Sabbath isn't that interesting I mean they're watching him closely with evil intent to see if he does something good now Jesus was so famous for doing good that people began to try to catch him doing it and that's going on that goes on all the time I mean it even goes on now just to just to think of his out loud watching to see if someone does something good to accuse him for being bad that's kind of like what what's going on with nurses today being watched in case they do good many work throughout the pandemic without masks and now they're being watched I find that I gotta be careful with this I shouldn't have made that note to myself because it really bothers me it bothers me that people who are doing good are now being told that what they're doing if they don't put on a mask is bad it makes no sense these are people who are willing to put their lives on the line to care for people and now they're being penalized I don't know I don't know if we have any any nurses in this room I don't know if we do or not I know my son is one and I'm very proud of him in the Lord for for that and for all the work that he's done on behalf of other people but if we have any of those who are here any nurses medical practitioners we as a church just want to tell you we love you and we're grateful for the work that you've done I mean I don't understand this because they're being watched now and and and they're watched being watched to see if they do anything good and and they're trying to find him in violation of breaking the law of the Sabbath there's a man he's in need Jesus is there and he sees this and they knew that Jesus wouldn't avoid ministering to a hurting man well you see unless a person's life was in the balance the most you could do was basic care doing anything more was considered working it violated their tradition now Luke tells us that Jesus delivered a woman with the spirit of infirmity on the Sabbath the ruler of the synagogue became incensed when Jesus did so it's found in Luke 13 verse 14 and it says he was indignant because Jesus had healed on the Sabbath so the synagogue rulers said to the people there are six days for work so come and be healed on those days not on the Sabbath they looked at the healing as an act of work now you need to know that to violate the Sabbath there was a crime punishable by death Exodus 31 14 says observe the Sabbath because it's holy to you anyone who desecrates must be put to death whoever does any work on that day must be cut off from his people this is going to be a charge they can bring against him before the Jewish religious court and Jesus knew it he knew he was being watched and he didn't back down Matthew 12 10 tells us that they asked him is it lawful to heal on the Sabbath to accuse him and then in verses 11 and 12 of Matthew 12 it says that he said to them if any of you has a sheep and it falls into a pit on the Sabbath will you not take hold of it and lift it out how much more valuable is a person than a sheep therefore it is lawful to do good on the Sabbath Jesus knew that he was being watched but he didn't back down why because it is right to do good on the Sabbath when everything had been shut down and there were statements being made you can't gather together and we as a church observe the the rule that we should not be gathering and we did it for several weeks and then finally one day I was here and people started driving up because from from the very beginning when we returned from Israel it was the next week that everything was two weeks everything was shut down and I told my staff I said you know what we're going to have to observe this because we don't know what's going on we don't know what's happening I I'm not a doctor and we don't have any news and they're still trying to find out what's really going on with this this virus and all I said I'm not willing to put our our sheep in jeopardy I'm not willing to do that need more information and so what we did is we we followed the ordinance and we we stopped meeting but that doesn't mean I stopped because it didn't I started I kept coming to the church I came on Sunday you know didn't put it on Facebook didn't tell people where I was we just came in some of my staff were here also on Sundays for several weeks I would just come and when people would pull up on the in the driveway they'd see us they were surprised they would actually come to give their gifts we had a goppy boxes out and the people came to give their gifts and and when they came we had opportunity to visit with them and and so after a few weeks it was really hot and and about 150 or so people um did a little parade through through the the church and and uh and we were waving at them because they they knew we were here and so I remember just looking at them as they climbed off the car and they were just a crowd of people in the parking lot and and I thought you know um I don't like them out here in the heat so we took them into the into the the chapel and we said let's go on into the chapel and they all spaced you know apart and everything and Jared was here I said Jared lead them in some worship and so Jared led some worship and I went up and gave a devotion and and so that was you know a few weeks into this pandemic and the next week we were back and they showed up again before you know we had people sitting here in the sanctuary and Jared would come and he I didn't publish it I didn't let everybody know I wasn't shaking my fist in the face of the governor or the president I was simply saying these are sheep they need to be fed I and their pastor I love them and I'm going to feed them that's what we do that's what pastors because you have to do you have to do what is right what is right no I wasn't writing letters to the press they know by the way come and arrest me you know because they were threatening those things and that's when I made John the pastor the church in case in case somebody had to do time he knows how to do time the short stretch for him you got to do what is right you have to that's what Christians do never put you I will never put you to my knowledge to the best of my ability as a pastor I would never put you into any position of jeopardy to satisfy my anger that I can have over what I consider to be the unfair regulations that have been placed on the church in order to stifle what God wants to do but you know what God is greater than any regulation that man can ever put because here we are right now there are people in different countries watching us right now because we just went online and we took the gospel message online and we went on seven days a week and we're reaching people every day of the week so the COVID which was meant for evil God has intended it for good we've been able to reach more and more and more people through it but you have to do what is right whatever your conscience permits within the confines of what scripture and the spirit leads you to do and so Jesus was being observed and he was being watched to see whether he would do something good whether he would heal somebody on the Sabbath and it is always lawful Jesus said to do good on the Sabbath well notice verse 3 he said to the man who had the withered hand he said step forward he took the offensive he's about to do something and it's going to do it in plain view he knew that this kind of thing would eventually be used against him and John in chapter 18 verses 19 and 20 it says the high priest questioned Jesus about his disciples and his teaching and Jesus said I've I have spoken openly to the world I I've always taught in synagogues or at the temple where all the Jews come together I said nothing in secret so Jesus knew this would eventually be used against him and so he asked the question in verse 4 he said is it lawful on on the Sabbath to do good or to do evil to save life or to kill but they kept silent is it right to do good on any other day and if it is then why is it wrong to do good on the Sabbath because doing good is really what believers are supposed to do and Ecclesiastes chapter 3 verse 12 it says I know that there is nothing better for men than to be happy and to do good while they live in 1 Peter 2 15 it says it is God's will that by doing good you should silence the ignorant talk of foolish men well see Jesus says is it lawful to do good or to do evil to save or to kill what is it so they kept silent the question really is which of us is doing good me if I heal him or you if you keep him from being healed it's so revealing to note that they knew Jesus could and would heal this man and even though they knew it they still would have kept the man crippled sometimes hardness of heart blinds you they were calloused and they were hardened notice in verse 5 he looked around at them with anger being grieved by the hardness of their hearts and he said to the man stretch out your hand and he stretched it out and his hand was restored as whole as the other now this is interesting how they now it's put he looked around when it says he looked around at them that's literally saying he surveyed the room he he looked from one corner to the other is what he was doing surveying and you can picture Christ as he slowly looks at them one by one as his eyes for just a moment lock with those people you know when somebody surveys the room like when I teach when I teach I've had this happen to me before as someone sitting being taught it's one thing when that when the when the teacher is looking around he does a quick glance right it's one thing that's another thing when he locks eyes with you gets kind of weird it feels kind of odd because you begin to think is you know because you'll you'll be talking and then he just rests on you for a minute and it's like you get you get to feel weird I've had that happen before where the the speakers and for some reason maybe he just felt like looking at me because I'm so cute I don't know but he stared at me and it's just like I feel like wow this feels odd so when Jesus was doing that picture that for a moment he's looking at them one by one and each one of them would be withering under his gaze as he's looking at him because he's angry he's angry there's no doubt that his face revealed to them that he was angry this unbelief of the Pharisees angered him and grieved him so it says here that he looked at them with anger and I look that up now the word anger why did you use that word the word anger here is a justifiable passion and hatred for something so he is justifiably angry and hated something and it says he was also grieved that word grieved means to be moved by grief and sympathy to sorrow at someone to be anguished he was angry and he was grieved he was grieved because they were rejecting the only way to salvation and John 5 24 most assuredly I say to you he who hears my word and believes in him who sent me has everlasting life shall not come into judgment but has passed from death into life in rejecting him they were placing themselves under condemnation in John 3 36 John the Baptist said whoever believes in the sun has eternal life but whoever rejects the sun will not see life for God's wrath remains on him what is it that bothered him hardness the hardness of the hearts that word hardness literally and I didn't make this one up the word hardness original in the original language speaks of stupidity it speaks of callousness and stubbornness a stupidity a stupid callousness the word heart spoke of their thoughts and feelings he was grieved and angered by their callous thoughts and feelings it's the same kind of hardness their ancestors had when they were freed from Egypt instead of rejoicing at the freedom they were given they rebelled in the wilderness the writer of Hebrews in chapter 3 verse 15 says as as has just been said today if you hear his voice do not harden your hearts as you did in the rebellion so two things triggered his response of righteous anger and grief one is their fault finding their evil thoughts the silence at his questions and second their hardness of people's pain due to their religious legalism they would rather this man remain crippled than to break their traditions once again they were old wine skins not open to the wine of grace now I was sharing last week concerning the new wine and I didn't refer to Luke's concluding verse because in Luke chapter 5 verse 39 he had Jesus said no one having drunk old wine immediately desires new for he says the old is better so the old wine speaks of the old practices of life the religious life of the Jews of his day that included the opposite observation of Moses's law the dietary rules a sacrificial system and Jesus brought a fresh way of worship because he was fulfilling the requirements of the law in Matthew 5 17 it says do not think I've come to abolish the law or prophets I haven't come to abolish them but to fulfill them and the Pharisees didn't desire what was new for them the old was to be preferred the problem with that way of thinking was they chose legalism over love and their willful choice to reject grace and mercy grieved and angered Christ doing so they chose to live without compassion and they end up in final judgment that kind of thinking closes the door of grace for those who would enter in when I first got saved and and and all there was a time when when people had long hair I had longer when the guys had long hair and that was I've shared this before but I'll say this very quickly that there was there was a church in I could tell you the name of the church but I won't it was in another state and they had it was a very large church and and I remember reading about this church because I became interested immediately in the life of the church and all and I was reading about this one particular church that that when a hippie got saved they had a barber on staff so when the hippie got saved the first thing they did after praying to receive the Lord was take him into a room and cut his hair off and so there was this legalism that was very entrenched in the church when I got saved at that time and then when I went into ministry in the in the late 70s I was an assisting pastor and we rented a particular church and we wanted we it was a seventh day church they would meet on they would meet on Saturdays and left the the church open on Sunday and so we were able to to to rent the church but they would not allow us to have on the stage area they would not allow us to have electric guitars and drums and the reason was they said because that that was unholy instruments there were there were I don't know if I should tell you this but it's in its history this I don't know if you know this or not some of you may already know this others may not but you may not know this it was the music that we played as Calvary Chapel Ministries and others that played the similar kind it was called voodoo music did you has anybody ever heard that some of you have it was called voodoo music isn't that trippy voodoo music why voodoo because they said the drumbeat would put you into a hypnotic state then you could be controlled by the speaker it was I think the Greek word is it was crazy it was crazy because you could have drums and guitars in the fellowship hall we would do outreaches in a fellowship hall but we could not have electric guitars you could have string guitars you couldn't have you know acoustic but you could not have electric and you could not have drums in the main sanctuary because apparently God doesn't hang around in the fellowship hall he hangs around in the sanctuary and so for us that really was amazing and that was kind of my welcome into ministry where there are attitudes of people have that will stifle your outreach when our church first began because my my babies I my children were very small and when our church began we did not we did not practice and did not take the kids out trick-or-treating we didn't do that that wasn't something Marie and I did and so they didn't have that when the kids would come and knock on the door and everything they they were not out there with their little costumes and so I said you know I want to give the kids an opportunity to just enjoy the day and so that's what we began what we're called hallelujah parties and so we had a hallelujah party when our church is very small it was in October 31st and we we we actually celebrated by giving the kids opportunity to come and play games and dressed in bible costumes and all and that's what caused the people who were renting the church that we were renting renting the church to us the church that we were renting that's what got us kicked out because they said that Calvary Chapel Ontario is worshiping the devil and so they kicked us out of the church what we were trying to do is we were trying to reach the children give them an alternative you don't have to worship the devil you can gather together as kids play some games and enjoy yourself what's wrong with that well a lot of people think there's things wrong with that so this is the kind of stuff that quenches the spirit in reaching the people to do good is lawful we were not practicing satanism they thought we were you know but obviously we weren't what we were doing is giving the kids an option we weren't worshiping the devil with electric guitars and drum beats we weren't going into voodoo trances but that's what the church has done and and a lot of times people begin to wonder why why people get turned off from the church itself is because we add so many layers of weirdness that the people say I don't want to follow your rules and regulations you see one of the things that I loved about and I should just make this quick and I will one of the things I loved about my own pastor Chuck is he didn't like the hippies he didn't like the movement he didn't like any of the things about us but he loved us and because he did you know we we had opportunity to hear the gospel and it transformed our lives that's what the gospels intended to do and so when you put a lot of regulations on it and you tell people a lot of things that that's not in scripture but it's what you like oh I don't like the color of your hair therefore I don't think you should wear tattoos you know to this day there are people still arguing about tattoos oh that's of the devil that's of the devil and then there were girls that were getting their their their their tattoos on their lower back and I've teased about this before some of you most of you probably heard me say this you know they put a little hummingbird on their on their back you know they're we used to call it tramp stamp I don't know what's called now but you put this little hummingbird and I'd warn them I'd say listen that hummingbird's going to be a vulture you're going to grow as you get older and it's going to be aware of these things you know but I never went up and said you can't you can't do that you know why because that's adding to scripture they're taking Old Testament scriptures and and and twists in amount of context you don't have marks on your body as as a veneration to idols and false gods that's what that's what Leviticus said but here we go saying you can't have that you can't have long hair you can't have piercings I don't why I don't know why you want piercings I don't understand piercings that looks like it hurts and it does and some people when they walk by you know magnets a magnetist jump all over their faces you know I mean they get stuck on refrigerators all the time it's just we just have to be careful guys that we don't add to God's word our traditions is it lawful to do good or to do evil Jesus said it's lawful to do good now what's interesting here is I want you to see this and we'll close with this in verse five he was grieved by the hardness of the heart he said to the man stretch out your hand and he stretched it out and his hand was restored as whole as the other how could he do that his hand was withered it was paralyzed it was immobile he could he could have said Lord my hand is withered how then can I stretch it out heal me first and and then I'll do as you say because that's reasonable but in his case that would have been foolish you see the man was healed with a word without even a touch that means the Sabbath was unbroken even according to the most rigid interpretation of the letter of the law Jesus said stretch out your hand the man in faith stretched it out and it was completely restored as whole as the other he gave to him a command that for the man was impossible to obey when God gives a command he also supplies the ability to perform that which is commanded and he said to that man stretch out your hand and that man did the impossible so what is it that has crippled us today what is it that may have crippled you what is it that is keeping you from being what you know you want to be and what he wants you to be do you think that perhaps the Lord may be saying some of us today stretch out your hand do that which is impossible stretch it out whatever it may be and watch what God can do you know if you'd have asked me as a kid if you'd have asked me or told me one of these days you're going to stand in front of people and you're going to talk about God if you'd have told me that I just said you're crazy if you'd have told me that one day I was going to stand in front of people for all these years and share the same message with people I just said that's not going to happen because in my own heart I was crippled but when the Holy Spirit brought his healing to me he made it possible for me to stretch out my crippled hand he made it possible for me to do that which personality wise was really not possible because those of you who know me as a person perhaps on a level outside of just sitting in the view you will know that I'm very shy that I'm very quiet that I just kind of keep to myself because that's my personality that's how I am I only come alive when I'm behind a pulpit I only come alive and show emotion when I'm behind this pulpit that's when I do normally I'll just kind of it's made people kind of awkward around me in the past they'll see me and hi Pastor David how are you and I'm kind of reserved fine you know they're looking and sometimes I think that they think that I'm a snob and I'm really not what I am is shy I'm a shy snob but I'm I just say that in the event that I may see you someday out and because I I run into people quite often in the area and you may be a bit surprised that how reserved I actually am because it's the Holy Spirit that makes me come alive with his word and I've had to learn to stretch out my hand a long time ago to say I'm going to break through see I don't even you may believe this or not I don't show emotion at home I don't I only show up with you guys when I tell you my heart that's me I'm very reserved forgive me for even the motions I show it's hard for me to do that but God told me a long time ago stretch out your hand and I'll make you whole maybe somebody in this room needs to learn to stretch out yours because God wants to do something in you too beyond anything you could ask a thing he wants to use you just be available if he says it do it and then give to him all the glory for that which might come can you do that I hope that you can our father we would ask that you would work in us today Lord you are the Lord of the Sabbath and you have made it as a day of rest a day that we gather together to to worship you a day that we gather together to learn of your word and and to put it into practice a day that we learn to to love you and as a result to just basically overflow with love for other people a day that we center our attention on you a day that we can put into practice daily so I asked Lord that we might learn to to worship you and to love each other and I asked that you would work in us Lord so that we might be living lives that are pleasing to you and even as our eyes are closed and our heads are bowed perhaps the Lord is speaking to some here in this room we need to get right with him maybe you're watching online or you're in one of the overflow areas and the Lord is speaking you need to get right with him I want to pray for you and if you do would you raise your hand right now and let me pray for you right where you're at Father I ask that you would touch these whose hands are raised in Jesus's name I ask that you would reach then and touch them Lord wash and cleanse them work within them and have your way Lord move upon them they may be carrying a burden right now or hurt of some sort or dealing with something that has injured them whatever the case may be I pray that you would just be there heal them and minister to them as they stretch out their hand to you right now I pray that you would reach down and touch them we lift them to you now Lord and we thank you because Father you are the God of answers prayer and we thank you for this and bless you can put your hands down and last time we were together and I feel I want to do it again I feel it's something that we should do right now last time we were together there were some I asked if there's anybody in need of being touched by the Lord physical healing of maybe an emotional healing and you just your body is responding right now in a way that just isn't good and you need you need to touch them but what I want to pray for you and if you if you want prayer for that would you stand up and let me pray for you right where you're at just stand so I might see you Father you see these who are standing right now Lord you know you know what's going on in hearts right now and bodies you know the things that we're going through health wise there are so many that are ill at this time Lord in Jesus name may your hand of healing touch them and mercifully and compassionately Lord I pray that you would work a miracle in them right now Lord by faith we're saying God would you please touch us Lord in Jesus name would you bring healing and I ask that you would Lord because you are the healing God you are the God our healer and we simply cast our cares on you now and ask for your hand to touch and bring healing Lord and by faith we would receive from you and we stretch out our hearts to you right now that you might reach us we give you praise for this and receive the Lord and thank you and bless you thank you you can you can be seated and Jesus I just pray that you continue to move in all of us to your glory in your name amen


In the previous lecture we introduced a model for wireless transmission, in fact if we go back that we have a signal that we want to transmit from transmitter to receiver and a simple model is we transmit an electrical signal with some power level, some strength. If you think of the sine wave as our signal, then the amplitude of that sine wave is the power. So that's the signal strength, how large it is, that's Pt, we denote that power as. But we use antennas to convert that electrical signal to radio waves or electromagnetic waves that propagate through the air. And we're talking about antennas and we arrived at some description of the antenna gain. We have the basic or the reference antenna called an isotropic antenna that when we transmit the energy comes out of that antenna and goes in all directions equally. Let's think of that as the perfect antenna. But in practice we use directional antennas even though we may be very close to an isotropic antenna and the power is concentrated in a particular direction. So instead of spreading equally in all directions the power will be strong in one direction, weaker in another direction. And we talked about that if we measure in a particular direction our directional antenna versus the isotropic antenna we can compare them and we can say that the directional antenna has some gain compared to the isotropic antenna. So we talked about that concept and it's a key characteristic of antennas. The antenna gain usually specified in the direction where it's strongest. So the gain changes in different locations for a particular antenna but in that direction where the signal is strongest we'll see a speck of that antenna is the antenna gain. Measured in dB usually decibels. Decibels and the I indicates the decibels of our antenna relative to using an isotropic antenna. That's why we write it as DBI. We say we're comparing ours relative to some reference isotropic antenna. And we went through an example where we looked at two different points for our blue directional antenna and this was a made up example for an antenna where we set up the red point, point X if we used our black isotropic antenna the signal strength received would be 10 milliwatts anywhere on the black circle 10 milliwatts. If I use my blue directional antenna the signal strength received let's say we measure to be 70 milliwatts. So at that one point our directional antenna is 7 times stronger than the isotropic antenna and that gives us the gain. A gain of 7 or in dB 8.45 dBi. Just the conversion of logarithm times by 10. And we could think for my blue directional antenna this is a part of the speck for that antenna. When I go looking to buy one I see this antenna has a gain of 8.45 dBi. We'll see how we'll use that later. But in fact the antenna in different directions has different gains. So we looked at the point behind the antenna at point Y. On the black circle the measured received power would be 10 milliwatts for the isotropic antenna but with our blue directional antenna on that same point PY let's say we measured it to be 2 milliwatts then our gain is 0.2. It's in fact a loss. The signal strength of our antenna compared to an isotropic antenna is less than the isotropic antenna 2 divided by 10 0.2 or minus 7 dBi. And if we measure to other points 1 meter away we could determine the gain. So usually for an antenna we list at least the maximum gain like in the direction with the maximum signal strength and sometimes we'll see pictures that show the gain in different directions called antenna patterns. And I'll show you a few examples of them where Cisco is a company that makes computer networking equipment and they make and sell some antennas and the reason I'm going to their web page is they have a nice web page that describes what are antennas especially related to Wi-Fi. So they have this guide on antennas and of importance for us they list the specs of their antennas. So I'll just show you some examples and I've just scrolled down to the actual specs maybe I'm at the wrong point. So they show some of the antennas that they sell and some of the specifications for them. So this first one is called a dipole antenna. Antennas have different shapes, shapes and sizes and the shape and size impacts upon the maximum gain and also the direction where the gain is strongest. So this dipole antenna is one of the stick antennas stuck on the access point on the wall. It has two dipole antennas. It has a maximum gain of 2.2 dBi. So that's typical for those access point antennas and if we scroll down a bit we see that that antenna the maximum gain is 2.2 dBi but in different directions it would have a different gain and the way that the specs capture that is via these two plots here. It's hard to draw in 3D so we draw two different plots one for each of the different planes. So the azimuth plane is the direction if we go on the horizontal plane around us. Elevation plane is up and down. So I think that if we have this antenna and we look in front of it to the left to the right behind and we measure the gain at points around it then this red plot shows us approximately in all directions going around that antenna the signal strength or the gain is about the same. We'll see some different ones later. So the gain we're not going to ask you to read these in an exam or a quiz but just to explain antenna gain this is showing that the gain in all directions all 360 degrees around that antenna is about the same. But if you look up and down from that antenna if you have the antenna here and you look direct in front versus up the way to interpret this blue plot is that direct in front is this 0 degrees here as we go up to maybe 30 degrees the antenna gain directly in front is about the same as 30 degrees up. But as we go up to say 60 degrees at this point if you measure at the same distance away the gain will be less the way that it's coming in. And if you measure directly above that antenna the gain will be very small. That's what this plot shows. So directly below the antenna at this point indicates that the gain is very small. This shows the gain in two dimensions on two different plots if you combine it what sort of shape do you get if you try and draw this as three dimensions and maybe you have it on your slides. A donut. You can imagine that in all directions around it's the same but up in that direction is about the same but if you go directly above it it's very weak so it sort of creates a hole just above it and just below it and it sort of becomes a donut type shape if you combine them. So that's the characteristics of a typical antenna on an access point. Most antennas are designed to work at a specific range of frequencies so this one is for 2.4 GHz. The typical Wi-Fi frequencies it's a Wi-Fi antenna and there may be other characteristics. Let's look at some more. Just another dipole antenna let's find some different ones different shape antenna, a monopole different design same gain, maximum gain of 2.2 dBi but the shape and it's hard to see they've superimposed the red and the blue on the one plot but the shape is slightly different in terms of the radiation pattern it's not necessarily a donut type shape it's in one particular direction it's a bit stronger than behind that one's hard to see with a single plot we'll find another one a 5 dBi sector antenna larger maximum gain so the shape of this antenna the sector antenna implies that it's you stick it in a location and it tries to cover a particular sector say of a circle rather than covering all 360 degrees maybe it covers 60 or 120 degrees of that circle with a strong signal and the other parts of weak signal and if we look at the antenna pattern on the azimuth plane we can think directly in front strong signal, high gain and maybe across these 120 degrees the signal is strong but if you measure behind the antenna here the gain is much lower so behind the signal will be weak designed to concentrate the power in a particular sector of our circle and the elevation is slightly different in front sorry, in front and then if you follow up and around you will get weak as you go up and down similar to our dipole so antennas have different shapes different designs to try to cover different areas a sector antenna is commonly used in mobile phone base stations there's an antenna that points and covering these 120 degrees of the city and then another sector antenna for another 120 degrees for example a couple more, that's a different shape let's go down a 6 DBI wall mount antenna similarly you stick it on the wall and it tries to cover a particular direction again tries to concentrate narrowly in one direction so if we stick this wall mount antenna on the wall here we could select the antenna such that it will try and cover where everyone is sitting it doesn't need to propagate a signal out that direction because no one sits over there in the room so we could choose an antenna to cover the area we want to cover and if we go up at a larger antenna 8.5 DBI different type 10 DBI antenna and I think one 12 DBI antenna essentially all directions around about the same gain but very focused in this direction that is if you go up a little bit the signal will be very weak if you go down a little bit the signal will be weak maybe 15-20 degrees the signal will be very strong there's a very high gain and you can use such antennas to cover a large distance you point this antenna at the similar antenna at the other location and as long as they are aligned then they should be able to communicate across a large distance they need to be aligned because if they're not aligned they're not pointing at each other the signal strength may not be large enough to be able to communicate so the more concentrated their energy is the higher the directionality of that antenna the more you need to align it to point to the receiver so that they can communicate and I think that's all a couple of others 14 DBI and I just scroll down to a couple more back to a dipole this is 3.5 DBI the only difference mainly this is designed for a frequency of about 5 GHz 5.1 to 5.8 GHz what is that frequency range commonly used for? about 5 GHz anyone? what do you use it for? we use it some of you may use it sometimes maybe not so often but maybe your device supports it it's another Wi-Fi frequency Wi-Fi is commonly very common in the 2.4 GHz range but there's another frequency band of about 5 GHz so if you've got a new phone or especially an access point this one doesn't but a newer access point that will allow you to support either 2.4 or 5 it has different characteristics maybe the practical benefits of 5 GHz is there's less people using that frequency and less interference but sometimes less range it depends on your wireless device it will support both so just some examples of antenna patterns and real antennas and a few more on the slides just the 3D and also the antenna pattern plots any questions on antennas? so we looked at the gain and we calculated in our example the gain it was say 70 mW divided by 10 mW the problem with this approach is for me to know the gain of my blue antenna I need to use my antenna and also use an isotropic antenna and measure the signal strength at the same location what we would like is to be able to predict the gain before I build it this requires measurements to know the gain a designer of the antenna wants to be able to design one and predict what would the gain be especially in different directions so this approach is not practical to find the gain when someone designs an antenna because it involves it being built and compared to an isotropic antenna it turns out there is a mathematical relationship between the gain and the effective area of an antenna and that's given by this equation we'll explain effective area in the moment but it's related to the physical area of the antenna so the gain is equal to 4 pi times by the effective area of the antenna something to do with the size of the antenna divided by the wavelength squared so the gain depends upon the size of the antenna and the frequency that we use in the signal being transmitted by that antenna if you increase the size does the gain go up or down with all other conditions the same increase the size of the antenna put your hands up if the gain goes up increase the size does the gain go up or down hands up for up hands up for down if the size goes up the area is going to go up so the effective area we'll explain a little bit more in a moment but the effective area is related to the how much area that antenna component covers so it depends upon the size so generally a good rule to remember if the antenna size goes up and G will go up the bigger the antenna the bigger the gain what if the frequency goes up we transmit a signal with a higher frequency what happens to the gain for example we saw with Wi-Fi there's 2.4 GHz and 5 GHz if we change from 2.4 up to 5 GHz with the same sized antenna will the gain go up or down frequency up what happens to the gain hands up for up frequency up gain some uncertain hands anyone have an answer remember frequency and wavelength are inversely proportional wavelength lambda equals the speed of light divided by the frequency so if frequency goes up wavelength goes down if wavelength lambda goes down we divide by a smaller number G will go up higher frequency higher gain if all the other conditions are the same lambda is the signal wavelength so if we know the signal frequency we can find the wavelength what about the effective area what does that mean for me is what we denote as the effective area it's related to the physical size but antennas we saw have many different shapes so sometimes it's hard to measure the physical size of the actual antenna component so we don't have an easy equation to calculate the effective area it differs so we need to know something about the internals of the antenna design to know the effective area but we can approximate for some antennas a parabolic dish antenna I think we showed in a previous lecture those like satellite receiving antennas they're a dish shaped maybe if you have satellite TV or satellite internet or you have seen the receivers the big dish shaped receivers the shape is a parabolic antenna if you look at that dish then the area is about it's approximately the area of a circle it's circular shaped but it dips in the middle but if you look front on the area is about that of a circle so the physical area of a parabolic antenna is approximately pi r squared if we have a dish which is one meter in diameter the radius is 50 centimetres the area is about pi times 50 or 0.5 squared in terms of meter squared that's the physical area the effective area it depends actually on the design the components and how it's built as to what the effective area is but commonly it's about half of the physical area in an exam I may tell you I may say assume the effective area is 0.5 times the physical area but I need to tell you that so it may differ on different antennas we may use that in an example shortly so if we know the physical area we can often determine the effective area and then from that if we know the signal frequency we can determine the gain of that antenna and that's useful to know in our subsequent analysis we will do a couple of calculations towards the end today so that's about antennas the next thing is about how does our signal travel between transmit antenna and receive antenna how does it propagate and then how much power do we lose we'll talk about those two things how does a signal propagate if I transmit a signal let's say I turned off the microphone and I talk we can think the signal goes it spreads out and propagates almost directly but in different directions towards your ears well it turns out there are different ways at which signals propagate especially when we transmit across long distances at some of the lower frequencies some which we which we may not see so often in this course but are important to mention the way that a signal moves depends upon the frequency of the signals and it depends upon the obstacles in the way or nearby whether it will pass through different obstacles and the way that it reflects off different obstacles so there are three main propagation models two on this slide ground waves, sky wave and on the next slide we'll see line of sight and the first two we'll mention quickly but we'll not see very common in this course are especially relevant when we're transmitting a long distance thousands of kilometres a wireless signal if we're sending a signal with a frequency below 2 MHz so under 2 MHz it turns out when we transmit the signal the signal due to the magnetic field of the earth changes speed there's some pressure on the signal that changes the speed and also the impacts of the atmosphere or ionosphere causes that signal to effectively bend around the curvature of the earth what that means or what this picture is trying to show the black line is the earth we have two antennas that transmit and receive antenna let's say several thousand kilometres away from each other normally if we try to send a signal straight through from one to another it would be obstructed by the earth we cannot go through the earth the signal will not propagate very well but if we use below 2 MHz the signal bends around the earth it follows the curvature of the earth meaning that even if there are obstacles in the way such as the earth itself the signal can still be propagated to the receiver ground wave propagation allows us to communicate it across long distances and used in AM radio similar but for frequencies from 2 up to 30 MHz is sky wave propagation it allows us to cover long distances but there's different characteristics here the signal is really transmitted up and it hits the ionosphere and the nature of the ionosphere is that the frequency of those 2 to 30 MHz the signals bounce off, they reflect and they come down to earth and bounce back up and keep going and again allows us to transmit across a very long distance really covering around the earth and this is commonly used in international radio stations short wave radio sometimes it's called you can pick up radio stations from Europe maybe from America because the signal propagates around in this reflection type mode in our data communications like Wi-Fi mobile phone systems and others we'll see with data links usually we use higher frequencies than 30 MHz so these 2 don't apply mainly for radio communications like AM or short wave radio so what does apply for higher than 30 MHz what we call line of sight the transmit and receive antenna must be able to see each other by seeing imagine you stand at the transmit antenna and if you had perfect eyesight you should be able to see the receive antenna in particular the antennas cannot be spread so far such that the curvature of the earth means that the earth is an obstacle in between them if we bring the antennas around they'll be obstructed by the earth so line of sight is the common model that we will use it doesn't mean that we can't have no obstructions it just means that the signal effectively goes straight line of sight communications it doesn't curve around the earth so with Wi-Fi we consider it line of sight in this mode even though we don't have to physically see the receiver there can be a wall but the signal goes straight and that's the mode we will see commonly there are other aspects on how the signal propagates whether it's obstructed by water by different temperatures and so on so some signals cannot be successfully received at different times of the day at night or during the day because they are impacted by temperature by the atmosphere what we want to concentrate on now is when we transmit a signal how much power is lost between the transmitter and receiver how much is the signal attenuated so let's analyse that first we'll talk about a general model for how we can compare signal strength at the transmitter and receiver in terms of a wireless transmission we transmit a signal with some power, PT the transmit antenna has a gain and we think of that gain as like in any gain it multiplies the signal strengths if I transmit at 100 milliwatts and the gain is a factor of 2 then you can think what comes out of the antenna is 200 milliwatts it's a gain, it's a multiplier as the signal comes out of the transmitting antenna the signal gets weaker we said attenuation means the signal as it travels some distance always gets weaker by how much we care about and at this stage we'll denote by how much is the loss L or the path loss to be specific L means in this equation means if L is 50 it means from the transmitter to the receiver the received signal will be 50 times weaker than the transmitted signal so the loss is by how much do we lose the power so we can think we transmit a strong signal it gets weaker as it travels some distance it's received by the received antenna and then that received antenna also has a gain it effectively amplifies the signal and the result after that received antenna is what we receive the power as PR mathematically we can think we transmit a power at power level PT the transmit antenna introduces a gain of GT a multiplier the receive antenna also introduces a gain of GR another multiplier and the path loss is captured by the parameter L that reduces the signal strength so we divide by L the result is the receive power PR a quick example transmit one watt we know the antenna characteristics let's say the gain not in dB the absolute values let's just make some easy numbers is 100 and the receive antenna has a gain of 50 that is the transmit antenna compared to an isotropic antenna gives a signal which is 100 times stronger the receive antenna has a signal which is 50 times stronger let's say we know the loss is a factor of 1000 so we can think we transmit a signal and I cannot draw it to scale we start with a transmitted signal the transmitting antenna introduces a gain so it increases the signal strength then there's a loss so that as the signal propagates it gets weaker and weaker by a factor of 1000 so this is the gain of the transmit antenna this is the loss we start with the transmit power there's a gain according to the transmit antenna the signal loses power across distance then it's received and the receiving antenna introduces a gain which amplifies again and what we receive here is the receive power PR whatever we end up with is the receive power strength what is the receive power strength? what is PR in this example? these are absolute values so PR is our transmit power 1 watt times by the gains no units divided by the loss I didn't choose very good numbers normally the loss will be much larger let me fix that let's add a zero here so I just made up some numbers typically the loss in many wireless systems will see is very high compared to the other factors but not always so we transmit at 1 watt the antenna is as 100 times 50 or 5,000 the total signal strength lost as it propagates through the air is a factor of 10,000 so we end up at the receiver with half a watt in this case I assumed I knew the transmit power I knew the characteristics of the antenna gains and let's say I measured the loss how much power was lost 10,000 then I could calculate the receive power we'll go through another example in a moment these values, the gains are in the absolute values not db don't use the db value here for the antenna gain for example but we can easily convert to db remember db, logarithm in base 10 multiply by 10 and if you do that on this equation on both sides you take the logarithm and then multiply by 10 then really because the logarithm of two numbers multiplied together is the same as the adding of the log of those two numbers together and dividing by becomes subtraction what we get is that the receive power measured in db is the transmit power measured in db plus the gains in db minus the loss in db so if our values are expressed on the decibel scale we can use this approach sometimes easier so let's go through another example that uses some different values and also combine back to the loss and distance in a moment maybe first new example let's consider an example of using wifi the scenario is I've got my I've got two endpoints so I want to connect together I've got two wireless devices wifi devices I'm going to use 2.4 gigahertz is the frequency what I'd like to know is how far apart can I separate those devices such that they can still communicate let's say I put one wifi device here at sit or on the roof then I'd like to know well how far away can I go such that my other device the receiver can still communicate with my transmitter what's the distance that we can achieve let's try and consider that by using some realistic examples for wifi the scenario maybe you're living out in the country and you want to connect your house to your friend's house and to connect them you're going to use an access point like the one on the wall you have one at your friend's house one at your house and you set them up in a mode so that they talk to each other we'd like to know well how far apart could they be such they can still communicate here's an access point that we'll use we have a few of these downstairs in the network lab actually in the other building just some newer access points than the ones on the wall so let's look at the specs somewhere where are they here they are alright the specs of the data rates actually the wired data rates up to 1000 megabits per second on the wired ports let's focus on the wireless features this access point supports the two different frequency bands available for wifi 2.4 gigahertz and the 5 gigahertz sometimes you'll see the precise names like IEEE 802.11 B, G, N, A, C, A they refer to different standards for how wifi works data rates here denoted as signal rate for 2.4 gigahertz goes up to 450 megabits per second 1.3 gigabits per second if you use 5 gigahertz for our example what's important is first we'll go to transmit power when we transmit a signal what's the power of that signal well it says if you transmit a signal with this access point if you're in Europe so the standard in Europe CE and other regions is if you're using the 2.4 gigahertz frequency range you can go up to 20 dBm 20 dBm is 100 milliwatts you convert back to milliwatts which you know from your quiz is 100 milliwatts if you use 5 gigahertz you can go slightly higher 200 milliwatts if you're in the US the US standards they control how much you can transmit at maximum power levels goes up to what 1,000 milliwatts or 1 watt let's use the 20 dBm value as the transmit power we'll use that in our example our device can transmit at 20 dBm what the other thing we need to know is when we receive a signal what is the weaker signal that that device can understand and that's often referred to as the receiver sensitivity reception sensitivity here let's focus on 2.4 gigahertz we'll use that in the example if I transmit a signal from one of these access points to another then the receiver is designed such that if the signal received is greater than minus 77 dBm if we're using this particular standard at 54 megawatt per second if the received power is greater than this my device receives successfully if the received power is less than minus 77 dBm you think it cannot hear it you cannot receive and it differs depending upon the standards and the frequencies as to what this received sensitivity is think of it as the lowest power we can successfully receive let's remember this one, minus 77 dBm we'll need it to work out how much loss we can tolerate between transmitter and receiver let's write down those values we've got our access point at one location think of that as the transmitter and some other location we want to have the receiver same access point and we know the characteristics this one has a transmit power let's set it to 20 dBm and this one when it receives a signal the smallest signal it can successfully receive we don't notice PR the minimum value of PR we can tolerate is minus 77 dBm what we would like to know is how much loss can we have between the two devices how much power can we lose such that the signal strength will still be greater than minus 77 dBm so we'll try and determine the loss the frequency we're assuming is 2.4 GHz the next thing we need to know is about the antennas what's the gain of the antennas on these devices I'm not sure if it's specified on the web page sometimes it says, sometimes not I think in this case it doesn't show us the antenna gain but we may guess I've got one of these devices the antennas are slightly bigger than those dipoles on the access point but let's assume that they're still about the 2.2 dBi I think they may be a little bit larger but let's give it a number the antennas it doesn't matter that there are three we just focus on the gain of a single antenna let's set it to be about the same as the one on the wall which I know is 2.2 dBi and at the transmitter and receiver they are the same same device so we can say the gain of the transmit antenna like that first Cisco antenna 2.2 dBi and the gain of the receiver antenna is the same they don't have to be the same you can have different antennas at the transmitter and receiver and they can have different gains just in this case they turn out to be the same what is the maximum loss that we can tolerate such that these two devices can still communicate find the maximum loss in dB if we transmit at 20 dBm there's a gain of 2.2 dBi then we lose some power then there's a gain of 2.2 dBi at the receiver antenna and we must receive at a power of at least minus 77 dBm so how much power can we lose such that the received power is minus 77 dBm what's L note that all of the values we saw in the spec transmit and receive power also if the antenna gains are in the dB scale decibels so use this equation don't convert them to milliwatts absolute values that's too hard just use the equation here which will give you the same answer but faster I will not write the notation or the subscript of dB we just PR measured in dB is Pt plus Gt plus Gr minus L but be careful all of these values must be expressed in the decibel form so we want to find L rearrange if we rearrange we can calculate the loss and we know those four values Pt is 20 dBm Gt is 2.2 dBi so is Gr minus minus 77 dBm this is why it's sometimes useful to use the values in dB most of the specs for equipment will be expressed in dB and then just adding and subtracting is quite easily 22.2 24.2 plus 77 is a 101.2 dBm 101.4 dB not dBm just add them up let people catch up and write that down and then we'll answer some questions about it the common question that comes up now how did you add up these numbers when you've got dBm dBi and how did you end up with dB that's strange the important point to remember is dB is not our normal unit it's a measure of the scale that we use if you think about the units what are the units for power? watts power transmit power receive watts or with a prefix of milliwatts the units for loss and the gains there are no units they're dimensionless they're ratios or factors so even though we write dBi and dBm we can still add them up in this because in dB scale we can add the factor in the i just means relative to isotropic so don't be confused and think that we somehow need to change dBm into dBi no the transmit power measures watts receive power measures watts in this case it's milliwatts and milliwatts the others are just factors or ratios and because we're on a logarithmic scale we can add them together if you don't understand that then convert them all to the absolute values convert to milliwatts and back to the absolute values and do the multiplication and division and you'll see you'll get the same answer loss, gain really measured in dB if we convert back to the absolute value there are no units in them so what does this number tell us it means if I transmit a signal from my access point if there's a loss of 101.4 dB or we can convert that back to the normal value the absolute value is 10 to the power of 10.14 not in dB remember the we divide by 10 10 to the power of or take the logarithm of this value and then times by 10 to get dB so this is the inverse operation what does it tell us the signal coming out of the transmit antenna if it loses its power by a factor of 10 to the power of 10.14 it is what about 10 billion if it loses the power such that the signal going into the receive antenna is 10 billion times smaller than the one coming out of the transmit antenna then with the gain of the receiver we will receive a power of minus 77 dBm and the spec of my equipment said if I can receive minus 77 dBm it will work okay if it was less it would not work so we've determined what's the maximum loss we can tolerate such that these two devices can communicate questions on this so far why do we care about loss what do we want to know I want to know how far apart I can put them distance can I separate them by such that they all communicate well it turns out if we know the loss there are some relationships between loss and distance so we can use some models to find out well if the loss is 101.4 dB what distance does that correspond to let's go to that now so we'll continue that example and convert it to distance and there are different ways to relate loss and distance it depends it depends upon the obstacles between the transmitter and receiver the walls whether the signals bounce off walls whether there are people in between trees and many other factors but we'll start with a very simple model in the ideal case assuming there are no obstacles we're operating in perfect conditions we say in free space imagine we're out in space nothing in between transmitter and receiver then the ideal model is referred to this free space path loss equation which says the loss is equal to 4 times pi times the distance divided by the wavelength all squared we know what the loss we can tolerate we know L we can find the wavelength because we know the frequency therefore we can find D the distance that our two devices can separate by let's do that now use this equation to find D the free space path loss model tells us loss not in dB be careful L here is not measured in dB it's the absolute value equals 4 pi D divided by lambda all squared what's lambda? we'll need that what was our frequency? 2.4 GHz so we can calculate the wavelength let's do it here lambda equals the speed of light divided by frequency what's the speed of light? 300 million meters per second 3 by 10 to the 8 meters per second the speed of light is about 300 million meters per second nice one to remember the frequency is 2.4 GHz so 2.4 by 10 to the power of 9 hertz or times per second calculator time effectively 3 divided by 24 300 million divided by 2.4 billion is 0.125 meters that's our wavelength we know L it's 10 to the power of 10.14 we know lambda it's 0.125 let's find D and it's just a matter of rearranging this if you rearrange what do you get? D the distance is the square root of L square root of it let's try that bit better the square root of the loss times by lambda divided by 4p 4pi I will not write down the numbers we'll calculate direct the square root of do we have 10 to the power of 10.14 that was a loss not in dB but in the absolute value times by the wavelength 0.125 divided by 4 and divided by pi 1,168 meters is the distance 1,169 if we round up to an integer so what does this number tell us now? we've got two of these TP-link access points the one on the web page one at your home one at your friend's home we know the specs of the transmit power and the minimum receive power PT and PR we assume the antennas had a gain of 2.2 dBi that's a good assumption when we transmit a signal with a frequency of 2.4 GHz we've used our mathematical models in particular the free space path loss assuming there are no obstacles in a perfect environment we've determined that we can separate them by 1,169 meters if we separated them by say 1,200 meters we would transmit a signal the gains of the antenna and the loss across that distance would be such that the receive power would be less than our minus 77 dBm so greater than this distance if the distance goes up the loss goes up and it means the receive power will go down and the threshold for our receive power was the minus 77 dBm so your friend can be 1,169 meters away if you want to communicate with these two access points any questions? okay it's not finished time yet yes the lambda is the speed of light divided by the frequency 3 by 10 to the power of 8 divided by 2.4 by 10 to the power of 9 the gigahertz you need to learn some of my writing especially the number of 9 is this realistic? this says not just if we're going to our friend's house but if you have your wireless device this access point and your laptop if it had a similar antenna and similar characteristics you could separate them by about 1 kilometer and still have Wi-Fi access do you think it's realistic? or another way? do you think you can communicate with this access point in this room if you're 1 kilometer away? most likely not in reality we have many obstacles between the transmitter and receiver even if there were no walls we're out in an open field the atmosphere has some impact upon the attenuation and it's not as good as this this is the best case result if we're out in space with no obstacles so we call it the free space path loss model in reality it's going to be less than this but this gives us an approximate value if we're say in an open field but not very good if we're indoors walls cause big problems there are other models other equations that try to approximate if we're inside in this course I think we will not see them but the free space path loss model is quite easy this equation there are others there's some for inside a city with different obstructions and different reflections there's some for TV broadcasts say from a TV station to your home and there's some for indoor modelling that is when there are walls and ceilings and so on to try to accurately model how far can we transmit to produce a particular path loss? let's stick with free space path loss for now I have a problem my friend is 20 kilometres away from me not one kilometre his house is a long way away how can I communicate with him using the same access points we've bought the access points we went out and bought them we want to set up a link between our two homes but they are 20 kilometres away from each other what do we do? what could we do? to still communicate I can't move my home what could I do? I need to communicate with my friend via Wi-Fi I must have a solution what do you propose? do you get a job as an IT specialist and you set up Wi-Fi networks what do you tell me? what do you sell me as a solution? move closer? remember our calculations was that so one thing that we can change quite easily usually is the antennas the antennas introduce a gain a bigger antenna, a bigger gain bigger gain means that under the same conditions the received power will be greater if we amplify more the received power will be larger and in fact most of these access points the antennas screw off so you can take them off and you can attach a bigger antenna and you can buy bigger antennas let's try a calculation to finish today let's keep everything the same same transmit power same frequency, same receive threshold but let's change the antennas and let's say now we use a big dish antenna let's see if it works both the transmit and receive antenna let's remove the dipole antennas and attach a dish antenna which is a 50 centimeter diameter antenna we buy parabolic dish so we need to point it at the dish at the receiving end we set them up we want to know can we make the distance of 20 kilometers if we buy these two antennas let's assume just for simplicity the antennas are the same as the transmit and receiver so we only have to do one calculation so if I know my dish is a diameter of 50 centimeters what do I do next? what's the gain of that dish? we have a way to relate the antenna size the frequency or wavelength and the gain let's assume that we have our parabolic antenna we know the radius is 25 centimeters the diameter is 50 centimeters let's assume that the it's a circle it's not quite a circle the area it's not a flat circle but let's assume it's a circle so the area is pi r squared and let's assume just for this calculation the effective area is half of pi r squared that would depend upon the actual design of the antenna but it's a good assumption given that we'll use this equation to find our antenna gain the area is pi r squared what's the radius in meters? 0.25 note that we use meters here, convert the meters everything will be in the standard units that's the area and let's say that the effective area is half of that in the equation the area of our dish is pi times 0.25 squared the effective area for the antenna calculation is half of that our antenna gain 4 pi Ae divided by lambda squared we know lambda, we calculated before it's 0.125 we can plug in the value for Ae to get the gain g of our antenna Ae is a half of A Ae is pi times 0.25 squared I'll plug them in into the calculator and find the value 4 times pi the effective area is a half times Ae Ae is pi times 0.25 squared so let's just times it twice divided by the wavelength squared wavelength from before was 0.125 2 just plug in the values 79 about we get a gain of about 79 we'll write that down in a moment and if we want to express in DBI we can log that times by 10 or about 19 DBI 79 as the absolute value as the multiplier or 19 DBI is our parabolic dish antenna which is the same as 19 approximately DBI our dipole antennas were 2.2 we've changed the antennas we're up to 19 DBI for simplicity let's say the antennas are the same at the transmitter and receiver we need to calculate the gain separately what's our loss now the transmit power 20 DBM plus the gain of the transmit antenna 19 DBI plus the gain of the receive antenna also 19 DBI minus our minus 77 DBM anyone can calculate for me 135 dB convert to the absolute value 10 to the power of 13.5 we know the loss now what's the distance from before we're just using the same equations but different values this time square root of 10 to the power of 13.5 our loss times by our wave length 125 divided by 4 divided by pi did I get that right 55,000 56,000 meters our distance is about 56 kilometers by increasing the antenna gain using different antennas in this case they have a larger gain we can tolerate a larger loss to receive at the same power or in other words we can transmit across a larger distance to still receive at minus 77 dBm so we achieve our link between our two friends check the calculations of those we will summarize in the next lecture and finish on this wireless transmission so you should be able to do some calculations of path loss antenna gains and similar we'll continue tomorrow


Good afternoon folks, Steve Rhodes coming to you live from the shores of Delray Beach, Florida. This is your 2PM update and currently a mixed bag out here, the Dow trading down 57. The S&P is up three, the NASDAQ up five, the Russell is flat, some eyes up three. That's flat. You've got gold flat trading 1783, silver's basically flat. It's kind of a flat market. So let's do this. Instead of looking at our indices out here, which we typically do, let's go take a look at the sectors inside the S&P 500, kind of get a feel for what they're communicating to you and I. Now, I say the sectors, but we're first going to start with the four equity future, the four ETFs, the Qs, the spies, the diamonds, and the IWM. The Qs have a nice arrangement to mitigate our top support is held, much like the NQS new profile. So to the Qs support there being 39, 391, 99. The S&P 500 still has a TD9 count top in place, but support has held and that's the bottom of its profile, 46560. The Dow Diamonds had a TD9 count top that led to price testing the TD9 breakout support at 355.75 yesterday was a bull sash candle that completed a Gartley buy pattern. The IWM is not trading that support. Support on it would be at 223.73. Today is going to become bar number six of a TD9 count. Looks like the IWM wants to head lower. To the XLK, a rose mint indicator top, price found support. That was the bottom of its daily profile yesterday. The XLV, no top, just a sideways consolidation inside its profile. The XLF, kind of neutral at this stage here. It's got resistance of 4036. It gets to its bullish modes of price can close above that. The XLC, the communications sector, looks like it wants to head lower. So of these eight that we looked at, it's the XLC that says that it wants lower price. If we switch over from this set of charts to the other sectors inside the S&P 500, let's go take a look at the energy sector, the XLE. What is it doing? Right into resistance, that's the oscillator and change line. If it can close above that, it'll run to 58.59 and above 58.59 on its merry way. The XLY, no topping signal out here, just price consolidated with inside its daily profile. Support at 205.82. The industrial sector has got a rose mint indicator top, has led to a sideways consolidation with price above the top of its profile. It is neutral. The XLP has a rose mint indicator top. Price ran into resistance yesterday at the top of its daily profile. It's just in a sideways type consolidation. The XLU has a TD9 count top, but if price can close above the TD9 count top high, which is at 67.84, it'll be on its merry way to a much higher price, about 70 or so. The XLB out here, a TD9 count top, it remains bullish because price above the top of its profile as well. The real estate sector trying to take out resistance says it wants to head to higher price. Folks, have a wonderful Wednesday. Stay tuned for more great programming.