Welcome back to electronics. This is Dr. Robinson. In this lesson, we are going to look at a diode envelope detector circuit. In your previous lesson, you were introduced to voltage regulators and our objectives for today's lesson are to introduce amplitude modulation and demodulation and introduce an envelope detector circuit. Amplitude Modulation is the modification of the amplitude of a waveform by variation of a second waveform. Now these wave forms can be any sort of wave form, a triangle wave, a square wave, but let me show you how we would form an amplitude modulated signal from two cosine waves. Here are the equation of a wayform that I'm referring to as the carrier signal. You can see that it is a cosine function that varies between plus 1 and minus 1 at a frequency of omega c. We multiply that by an amplitude A so the overall carrier signal varies between plus A and minus A. Now here's a second cosine function that I'm referring to as the message signal. Again, it has an amplitude, this time equal to k and it's varying at a frequency of omega m, the message frequency. Now if we combine these two signals in this way, we form an AM modulated signal where the AM modulated signal s(t) is equal to 1+m of t, all times c of t. Now in a cosine function like this, the quantity here in this position is the amplitude. And in this case, it's a constant a, it doesn't vary with time. But in the AM signal, we can consider this entire quantity here to be the amplitude of this cosine wave and you can see that this amplitude is now time varying because of this cosine function m of t. So the amplitude of this cosine varies at a frequency of omega m while the signal here is varying at a frequency omega c. Now k here is known as the modulation index. And it typically varies between 0 and 1. So in this particular signal for example, let's say that k is equal to 1. Then this quantity here would vary between 2 and 0, which means the amplitude of the AM modulated signal varies between 2A and 0 as time changes. But let me clear this up by showing you some pictures. So here on this voltage versus time graph, I've plotted both the carrier waveform and the message waveform. For this particular case, I've chosen a carrier frequency of 10 kilohertz and a message frequency of 100 hertz. And typically when forming and AM modulated waveform, the carrier frequency omega c is much much greater than the message frequency or modulating frequency, omega m. So in this case, there's factor of 100 difference between the message wave form and the carrier wave form. So when these two wave forms are combined together we get the AM modulated signal. It has an equation of this form, and you can what has happened. We still have the carrier varying at 10 kilohertz but the amplitude of that signal is varying now at 100 hertz. If we connect the peaks or maximum values of the AM modulated wave form and all of the minimum value just together. We have what's called the envelope of the AM modulated wave form or the AM signal. Now one of the primary uses of AM modulation is an aiding in the transmission of information. So if I were standing in a room full of students and the students in the back couldn't hear me I could increase my volume, I would speak louder so that they could hear the information that I'm saying. If I needed to cover greater distance, we can use electronics to aid in this transmission of this acoustic information. I can speak into a microphone, that acoustic signal, can be converted into electrical signal. We can use electronics to amplify it then apply that amplified signal to a transducer, a loudspeaker to again produce an acoustic way of this mechanical vibration that contains information. Then because we've increased the amplitude of the signal at the source, the signal will transmit further before its amplitude is attenuated below the threshold of hearing. But if we wanted to cover miles and miles of distance, transmit this information, a good way of doing that is to encode this audio information, these frequencies that vary from about 20 hertz to 20,000 hertz on top of an electromagnetic wave. We could amplitude modulate a high frequency carrier wave with my voice, the information we're trying to try to send. Then broadcast that electromagnetic wave using a high powered transmitter and a large broadcast antenna. We would receive that Signal far away using a receiving antenna attached to the front end of an AM radio, the AM radio would then decode or demodulates the carrier signal and recover the audio information. Now, in AM radio transmission the carrier frequency is typically much, much larger within the acoustic information, remember audio information is somewhere between 20 hertz, and 20,000 hertz. While the carrying signal in AM radio is approximately a half a megahertz to 1.5 megahertz. Now this high frequency carrier allows better propagation of the signal. It allows smaller receiving antennas, and a big difference between the modulating way form and the carrier wave form allows the modulating waveform to be more easily decoded or demodulated. Now, a second use for AM modulation is in creating sound effects, for example guitar pedals and we'll talk more about that later on. In an AM radio signal, the carrier carries the message and the message is contained in the envelope of the the AM modulated signal. So to extract the information we're interested in, we can use a circuit called an envelope detector, whose output is the envelope of the the input AM waveform. Now the circuit I've drawn here, you probably recognize from previous lessons. I've labeled the slid as Envelope Detector, but this is not actually an envelope detector. It's a portion of an envelope detector, and do you recognize it as being a halfway rectifier. In the circuit, I have labeled R1 as a one micro om resister. And the reason is I want to keep it here as a place holder to indicate that you could put a resistor here to form a voltage divider to make the output smaller than the input voltage. But in this particular case, I want the gain of the divider to be close to one. So I've made the value of R1 negligible relative to R2. So if we apply the AM modulated wave form that we've been talking about on previous slides to this half wave rectifier, do you know what the output would look like? This is a positive halfway rectifier and as usual if you want to pause this slide and think about the answer before I give it to you, I don't mind at all. The output wave form will look like this. We simply keep the positive half of the wave form and any portion of the wave form that's below zero volts if this were an ideal diode is eliminated. Now to extract the envelope from this way form we modify the circuit slightly. Here's the modified circuit, and you can see the only change has been the addition of this capacitor in parallel with the output resistor. Now, let me just show you qualitatively how this circuit works. As the AM waveform goes positive, this diode will become forward biased. And because this resistor is small, essentially a short circuit, the output capacitor will be connected directly across the input wave form. And it will charge up to the input AM value. Then as the AM voltage decreases with time, eventually this voltage on the capacitor will be larger than the voltage here on the input. The diode would be reversed by us, this portion of the circuit becomes an open circuit and the voltage on the capacitor can then discharge through the resistor R4 at a rate determined by this time constant R4C1. Now, that cycle repeats over and over again. As the AM waveform increases so that the voltage becomes greater than the voltage on the capacitor, the diode will turn on again and the capacitor charges. Here, I'm showing a zoomed in waveform. In red, we have the half wave rectified AM signal and in green, we have the output voltage or the voltage across the capacitor. You can see as the AM waveform increases, the capacitor charges up then as the AM waveform begins to decrease as time increases, the diode turns off and the capacitor discharges at e to the minus t over tau. Charge, discharge, charge, discharge, and you can see what's happening here, the green wave form is tending to follow the envelop or peak amplitudes of the carrier signal, if we zoom out you can see it better. Here in this graph, I have a zoomed out version of the rectified AM signal and the capacitor voltage. You can see that the capacitor voltage is following the envelope or the information or the audio signal that we're interested in. So the output of this circuit would look like this. It's the 100 hertz message signal with some 10 kilohertz variations in that. Now both 10 kilohertz and 100 hertz are in the audio range, so we could probably hear this small 10 kilohertz variation riding on top of the 100 hertz message signal. But typically in AM radio remember, this variation would be a half megahertz, maybe a megahertz. So that's far outside the audio band, so we wouldn't detect these variations, we would only hear this signal that's in the audio band. Now an important consideration in designing circuits like this is the time constant set here. If we made this time constant too fast then instead of tracking the envelope of the signal, we would tend to track the carrier. The capacitor charges up but then can quickly discharge, charge back up, quickly discharge, charge back up. So instead of following the envelope, the information we want to extract, we follow the carrier signal which is not helpful. If in the other extreme we make the time constant too large, say we made it infinitely large. I made this resistor infinity so that when the diode turns off this capacitor could never discharge. Then look at what would happen, AM wave form increases the capacitor charges to that value and then retains that value, charges retains that value, charges retains that value, until we reach the maximum value of the AM waveform. Let's look at this graph. Charge, charge, charge, and then it retains that value forever. And the output actually becomes a DC voltage with an AC input. And you could consider that circuit, with the very large time constant to be able to call it a peak detector circuit. If outputs a DC voltage that is equal to the peak value of the input way form. But again, if the time constants too large that DC voltage obviously doesn't attract the envelope they were interested in extracting. Now this circuit with a very large time constant. You've actually seen that circuit before. Remember when we talked about AC to DC conversion. We had input sign wave to possibly a transformer. Then to a rectifier, then Through a circuit with a large time constant or a large capacitor, large CAP. And the result was that the output voltage here was a DC voltage. So these three circuits that we've looked at before or I've mentioned, the peak detector, the AC to DC converter and the envelope detector are all essentially the same circuit but their purpose varies. Now, let's take a look at some actual AM wave forms and out puts of an AM envelope detector that I've built. So let's look at how an actual envelope detector responds to that AM modulated wave form that we've been talking about. Here I'm showing on the sole sub screen a 10 kilohertz sign wave, the carrier signal. And let me turn on the modulating signal, the 100 hertz signal and let's see what that looks like. Change the timescale to five milliseconds and you can see that the envelope has been formed when I turned on the modulating signal. We now have a 100 hertz envelope riding on top of the 10 kilohertz carrier. Now I'm going to apply this signal to the input of the envelope detector. First with no capacitor in the circuit so it acts just as a half way rectifier. So let me connect the scope to the output of the half way rectifier. And you can see the half way rectified modulated signal. The lower portion of the wave form has been removed. Now I'm going to add the capacitor to the circuit, so that we have a time constant that should if we picked it correctly track the in flow of the input signal. There we go. So by applying that AM modulated wave form that I showed you to this circuit, we extract from that a 100 hertz signal. Now let me connect that 100 hertz signal to a loudspeaker so that you can hear it So there is the 100 hertz tone and possibly on top of that 100 hertz tone you can hear a 10 kilohertz tone, it's a very high frequency tone embedded in that because the carrier is at 10 kilohertz. Let me remove the capacitor so you can see what the sounds like. So this will be just a halfway rectified AM signal. The variations there were at ten kilohertz so it sounded as though it was at a much higher frequency. But after demodulating by adding that capacitor you can hear that the primary frequency component now is at 100 hertz. So it does extract the information we're interested in, this simple diode circuit. Now another possible use for AM modulation, I told you was for sound effects, possibly as a guitar pedal. So rather than these pure sine waves that we're looking at as an input, we could apply the output of a guitar to an AM modulator to introduce a tremolo effect. So let me turn the frequencies way down or make them much lower so you can actually see and hear at the same time how AM modulation works. So I'm going to turn the carrier frequency down to 200 hertz. >> [SOUND] So there's a 200 hertz carrier signal, and I'm going to modulate that I'm going to turn the modulation on, do you hear the difference? Currently, it's being modulated 100 hertz, I'm going to turn that down to a very slow modulated frequency so you can see [SOUND] on the scope screen the modulation. [SOUND] There we go, so we have a 200 hertz carrier being modulated by a 1 hertz waveform. And you can see how the amplitude of the carrier on the scope screen is varying slowly, one time per second, so you get that very slow tremolo effect. Now let me turn up the frequency of the modulating wave form. [SOUND] So now with this scale on the scope, you begin to see the envelope. Let me change the scale. [SOUND] There we go. So now you can see above the carrier in the envelope, we're now modulating at ten hertz, I'll continue to increase the modulating frequency. [SOUND] So there's what you probably call tremolo and again imagine that instead of applying true sound waves, you're applying a guitar input and you could control frequencies is with the change in pedal location, or change in a possibly a potentiometer. [SOUND] Let me try changing the carrier frequency so you can see what happens. [MUSIC] So that is a 1 kilohertz sound wave with a 21 hertz modulating signal, and you can definitely hear the tremolo effect. [SOUND] So you can imagine that by varying both the carrier frequency, and the modulating waveform frequency and amplitude, you can get all sorts of effects. So think science fiction movies or 80s video games. [MUSIC] I'm varying the carrier frequency from about 700 hertz down to 300 hertz. [MUSIC] So in summary, during this lesson we introduced amplitude modulation and demodulation and we examined diode envelope detector circuit. So thank you and until next time.
