WEBVTT NOTE This file was exported by MacCaption version 7.0.06 to comply with the WebVTT specification dated March 27, 2017. 00:00:00.208 --> 00:00:04.917 align:center line:-1 position:50% size:67% Hi, my name is Matt Ozalas, and I'm an RF engineer at Keysight Technologies. 00:00:04.917 --> 00:00:09.667 align:center line:-1 position:50% size:51% In today's talk, I'll go over the basics of how to design RF power amplifiers. 00:00:09.667 --> 00:00:12.708 align:center line:-1 position:50% size:46% I think that this material should give you a good foundation 00:00:12.708 --> 00:00:15.500 align:center line:-1 position:50% size:44% for understanding how these types of circuits work. 00:00:15.500 --> 00:00:18.583 align:center line:-1 position:50% size:40% If you understand the material that I'm going to cover today, 00:00:18.583 --> 00:00:21.667 align:center line:-1 position:50% size:49% you'll also be able to build off of it to understand more advanced topics 00:00:21.667 --> 00:00:24.208 align:center line:-1 position:50% size:41% in the field of power amplifiers. 00:00:24.208 --> 00:00:29.917 align:center line:-1 position:50% size:60% The objectives of my presentation are first to define power from an AC perspective, 00:00:29.917 --> 00:00:35.792 align:center line:-1 position:50% size:62% and then demonstrate how power is generated and dissipated in a real power amplifier circuit. 00:00:35.792 --> 00:00:39.958 align:center line:-1 position:50% size:58% Next, we'll look at power amplifier operation from an intuitive point of view. 00:00:39.958 --> 00:00:43.333 align:center line:-1 position:50% size:32% I'll build off this to define and discuss efficiency. 00:00:43.333 --> 00:00:45.417 align:center line:-1 position:50% size:49% From there, we'll look at how to set up a loadline, 00:00:45.417 --> 00:00:48.250 align:center line:-1 position:50% size:46% and how this is used in PA design. 00:00:48.250 --> 00:00:50.000 align:center line:-1 position:50% size:66% I'll even share my Workspace with you at the end 00:00:50.000 --> 00:00:54.917 align:center line:-1 position:50% size:62% so that you can explore the concepts that I'm going to talk about today at your own pace. 00:00:54.917 --> 00:00:56.917 align:center line:-1 position:50% size:37% Now, part of the Workspace that I'm making available 00:00:56.917 --> 00:00:58.958 align:center line:-1 position:50% size:56% will be an interactive waveform generator, 00:00:58.958 --> 00:01:04.542 align:center line:-1 position:50% size:66% which will allow you to design, generate, and analyze your own RF waveforms in real time. 00:01:04.542 --> 00:01:09.042 align:center line:-1 position:50% size:66% This will help you to understand these key concepts that we're going to talk about today. 00:01:09.042 --> 00:01:12.583 align:center line:-1 position:50% size:56% All of the waveforms and examples that I'm going to show in this presentation 00:01:12.583 --> 00:01:16.708 align:center line:-1 position:50% size:55% were generated using this waveform tool. 00:01:16.708 --> 00:01:21.500 align:center line:-1 position:50% size:67% To understand RF power amplifiers, we need to begin with an understanding of power. 00:01:21.500 --> 00:01:25.875 align:center line:-1 position:50% size:57% Most RF engineers are familiar with power from a frequency domain perspective. 00:01:25.875 --> 00:01:27.917 align:center line:-1 position:50% size:47% To be successful as a PA designer, 00:01:27.917 --> 00:01:32.125 align:center line:-1 position:50% size:49% you'll also need to understand power from a time domain perspective. 00:01:32.125 --> 00:01:36.250 align:center line:-1 position:50% size:60% Here, I'm showing a set of sinusoidal voltage and current waveforms in the time domain. 00:01:36.250 --> 00:01:39.083 align:center line:-1 position:50% size:43% Each of these can be described simply by sine wave equations 00:01:39.083 --> 00:01:42.208 align:center line:-1 position:50% size:58% with an amplitude offset and a phase offset. 00:01:42.208 --> 00:01:46.167 align:center line:-1 position:50% size:58% We can obtain the average power from this by multiplying these waveforms together 00:01:46.167 --> 00:01:49.292 align:center line:-1 position:50% size:34% and calculating the area under the resulting curve, 00:01:49.292 --> 00:01:51.583 align:center line:-1 position:50% size:40% and then dividing by the time. 00:01:51.583 --> 00:01:54.458 align:center line:-1 position:50% size:40% Now, for the waveforms described by these equations, 00:01:54.458 --> 00:01:59.250 align:center line:-1 position:50% size:60% the interval works out to be simply a multiplication of one half of the peak values 00:01:59.250 --> 00:02:03.625 align:center line:-1 position:50% size:48% times the cosine of the phase offset between the voltage and current. 00:02:03.625 --> 00:02:06.667 align:center line:-1 position:50% size:43% The peak values are, of course, half of the peak-to-peak values, 00:02:06.667 --> 00:02:11.625 align:center line:-1 position:50% size:54% so we can also express this equation in terms of peak-to-peak waveforms too. 00:02:11.625 --> 00:02:15.708 align:center line:-1 position:50% size:49% Knowing both expressions for power can be quite useful. 00:02:15.708 --> 00:02:19.458 align:center line:-1 position:50% size:38% Here, I have a very simple circuit setup in the simulator. 00:02:19.458 --> 00:02:21.708 align:center line:-1 position:50% size:62% This is just a frequency domain power source. 00:02:21.708 --> 00:02:25.625 align:center line:-1 position:50% size:62% I'm going to combine this signal with a DC bias through a bias tee. 00:02:25.625 --> 00:02:28.708 align:center line:-1 position:50% size:36% Then, I'll run a harmonic balance simulation on this. 00:02:28.708 --> 00:02:31.792 align:center line:-1 position:50% size:45% In the data display, I'll look at both the frequency domain calculation 00:02:31.792 --> 00:02:34.500 align:center line:-1 position:50% size:54% and a time domain calculation for power. 00:02:34.500 --> 00:02:38.625 align:center line:-1 position:50% size:62% In the frequency domain, since I have both a DC and an RF component, 00:02:38.625 --> 00:02:41.458 align:center line:-1 position:50% size:41% I'll get a spectrum at the output for voltage and current. 00:02:41.458 --> 00:02:44.125 align:center line:-1 position:50% size:39% If I multiply the voltage and current spectra together, 00:02:44.125 --> 00:02:47.250 align:center line:-1 position:50% size:34% conjugating the current, I'll get a power spectrum. 00:02:47.250 --> 00:02:51.792 align:center line:-1 position:50% size:63% You can see that both the DC and RF elements are 0.5 W. 00:02:51.792 --> 00:02:56.375 align:center line:-1 position:50% size:60% Now, it's also easy to isolate the fundamental frequency component, as I'm showing here. 00:02:56.375 --> 00:02:58.500 align:center line:-1 position:50% size:50% If I want to look at only the RF power, 00:02:58.500 --> 00:03:01.917 align:center line:-1 position:50% size:53% I can easily do that in harmonic balance by just indexing it, 00:03:01.917 --> 00:03:04.750 align:center line:-1 position:50% size:47% and it turns out that this is a 0.5 W. 00:03:04.750 --> 00:03:08.458 align:center line:-1 position:50% size:55% In the time domain, I'll start by multiplying the voltage and current together. 00:03:08.458 --> 00:03:12.250 align:center line:-1 position:50% size:48% Then, I'll integrate the product and divide by the time to get power. 00:03:12.250 --> 00:03:14.417 align:center line:-1 position:50% size:45% In this case, I have 1 W of power. 00:03:14.417 --> 00:03:18.292 align:center line:-1 position:50% size:57% By the way, I get the same result if I just multiply the peak voltage and peak current 00:03:18.292 --> 00:03:20.000 align:center line:-1 position:50% size:22% and divide by 2. 00:03:20.000 --> 00:03:24.125 align:center line:-1 position:50% size:54% In other words, this integration produces the total power in the entire spectrum, 00:03:24.125 --> 00:03:27.833 align:center line:-1 position:50% size:66% which is a combination of both RF and DC power. 00:03:27.833 --> 00:03:29.750 align:center line:-1 position:50% size:46% What if I only want the RF power? 00:03:29.750 --> 00:03:34.750 align:center line:-1 position:50% size:63% Well, if I consider the peak-to-peak voltage and current signals instead of the peak signals, 00:03:34.750 --> 00:03:37.125 align:center line:-1 position:50% size:48% then I'm left with only the RF power. 00:03:37.125 --> 00:03:42.708 align:center line:-1 position:50% size:61% In the time domain, using this approach can allow you to easily separate RF from DC. 00:03:42.708 --> 00:03:46.042 align:center line:-1 position:50% size:54% Don't worry if you didn't catch exactly how I calculated all these things. 00:03:46.042 --> 00:03:49.583 align:center line:-1 position:50% size:62% Again, I'll provide a way to download this Workspace at the end of the presentation, 00:03:49.583 --> 00:03:54.417 align:center line:-1 position:50% size:69% and you can see exactly how I calculated the power in these different ways. 00:03:54.417 --> 00:03:56.958 align:center line:-1 position:50% size:45% The phasing between the voltage and current waveforms 00:03:56.958 --> 00:03:58.667 align:center line:-1 position:50% size:38% is really important for power. 00:03:58.667 --> 00:04:00.458 align:center line:-1 position:50% size:33% This is a cosine function. 00:04:00.458 --> 00:04:03.792 align:center line:-1 position:50% size:59% If I sweep the phase angle between the voltage and current waveforms 00:04:03.792 --> 00:04:06.542 align:center line:-1 position:50% size:37% from 0 to π, or 180 degrees, 00:04:06.542 --> 00:04:09.042 align:center line:-1 position:50% size:42% turns out that there's a maxima and a minima in the power, 00:04:09.042 --> 00:04:11.542 align:center line:-1 position:50% size:45% which just arises from the cosine. 00:04:11.542 --> 00:04:15.333 align:center line:-1 position:50% size:65% Now, at the maximum point, the voltage and current waveforms are in phase. 00:04:15.333 --> 00:04:17.958 align:center line:-1 position:50% size:59% This means that power is getting dissipated. 00:04:17.958 --> 00:04:23.125 align:center line:-1 position:50% size:61% In practical transistors, power dissipation acts to convert energy into heat. 00:04:23.125 --> 00:04:24.333 align:center line:-1 position:50% size:48% Now, on the other side of the graph, 00:04:24.333 --> 00:04:27.625 align:center line:-1 position:50% size:54% we have the case where the voltage and current waveforms are out of phase. 00:04:27.625 --> 00:04:30.542 align:center line:-1 position:50% size:47% In this case, we say that the device is generating power. 00:04:30.542 --> 00:04:33.708 align:center line:-1 position:50% size:56% In the middle of the plot, power is neither dissipated nor generated. 00:04:33.708 --> 00:04:36.375 align:center line:-1 position:50% size:34% Instead, it's being stored. 00:04:36.375 --> 00:04:40.167 align:center line:-1 position:50% size:62% Here's an example of a circuit that we're going to use a lot in power amplifier design. 00:04:40.167 --> 00:04:43.667 align:center line:-1 position:50% size:38% This is an AC current source which is tied to a resistor. 00:04:43.667 --> 00:04:46.083 align:center line:-1 position:50% size:68% Since these components are connected in parallel, 00:04:46.083 --> 00:04:50.333 align:center line:-1 position:50% size:50% the current source and the resistor share the same voltage across them. 00:04:50.333 --> 00:04:53.417 align:center line:-1 position:50% size:45% Since current source pulls current out of the resistor, 00:04:53.417 --> 00:04:56.000 align:center line:-1 position:50% size:65% the currents are opposite in the two components. 00:04:56.000 --> 00:04:58.875 align:center line:-1 position:50% size:53% For the resistor, the voltage and current are always in phase 00:04:58.875 --> 00:05:01.500 align:center line:-1 position:50% size:67% because they're simply related through Ohm's law. 00:05:01.500 --> 00:05:06.083 align:center line:-1 position:50% size:65% For the current source, since the current is going in the opposite direction as the resistor, 00:05:06.083 --> 00:05:08.417 align:center line:-1 position:50% size:55% the voltage and current are out of phase. 00:05:08.417 --> 00:05:10.917 align:center line:-1 position:50% size:57% The current source is the power generator. 00:05:10.917 --> 00:05:13.125 align:center line:-1 position:50% size:48% The resistor is the power dissipater. 00:05:13.125 --> 00:05:17.458 align:center line:-1 position:50% size:61% You can determine this simply by looking at the sine of the voltage and current product. 00:05:17.458 --> 00:05:19.708 align:center line:-1 position:50% size:50% If it's negative, it's a power generator. 00:05:19.708 --> 00:05:22.958 align:center line:-1 position:50% size:49% If it's positive, it's a power dissipater. 00:05:22.958 --> 00:05:27.375 align:center line:-1 position:50% size:58% Now, in any physically realizable AC circuit, there must be conservation of energy. 00:05:27.375 --> 00:05:31.458 align:center line:-1 position:50% size:66% Any power that's generated must either be stored or dissipated somewhere. 00:05:31.458 --> 00:05:32.875 align:center line:-1 position:50% size:33% For this simple example, 00:05:32.875 --> 00:05:37.208 align:center line:-1 position:50% size:62% the power generated in the source is equal to the power dissipated in the resistor, 00:05:37.208 --> 00:05:40.583 align:center line:-1 position:50% size:27% with nothing stored. 00:05:40.583 --> 00:05:43.583 align:center line:-1 position:50% size:52% Practically speaking, this type of circuit can be realized physically 00:05:43.583 --> 00:05:46.292 align:center line:-1 position:50% size:55% using a transistor connected to a resistor. 00:05:46.292 --> 00:05:50.583 align:center line:-1 position:50% size:59% Here, I have a small-signal transistor model, like you might see in a textbook. 00:05:50.583 --> 00:05:54.875 align:center line:-1 position:50% size:53% It takes the voltage at the input, and then multiplies this by a gain factor, 00:05:54.875 --> 00:05:57.625 align:center line:-1 position:50% size:54% and converts it to a current at the output. 00:05:57.625 --> 00:06:03.000 align:center line:-1 position:50% size:68% Like I showed before, the voltage across the load and the current source of the device are the same, 00:06:03.000 --> 00:06:07.750 align:center line:-1 position:50% size:55% at least for AC signals, while the currents are going in the opposite directions. 00:06:07.750 --> 00:06:11.083 align:center line:-1 position:50% size:48% There's a little bit of a problem here, it takes energy to get gain. 00:06:11.083 --> 00:06:16.417 align:center line:-1 position:50% size:70% To provide this energy, we need a DC power source, which will create a bias on the device. 00:06:16.417 --> 00:06:19.042 align:center line:-1 position:50% size:37% This DC bias will mean that the sinusoidal waveforms 00:06:19.042 --> 00:06:22.667 align:center line:-1 position:50% size:58% are centered around the DC operating point instead of 0. 00:06:22.667 --> 00:06:25.208 align:center line:-1 position:50% size:64% We can do a simple nodal analysis at the output 00:06:25.208 --> 00:06:27.625 align:center line:-1 position:50% size:42% and show that the current that's supplied by the source 00:06:27.625 --> 00:06:31.458 align:center line:-1 position:50% size:67% is the summation of the current through the device and the current through the load. 00:06:31.458 --> 00:06:33.042 align:center line:-1 position:50% size:36% Or, to put this another way, 00:06:33.042 --> 00:06:36.667 align:center line:-1 position:50% size:53% all of the power that's used in the circuit to provide gain and output power 00:06:36.667 --> 00:06:40.417 align:center line:-1 position:50% size:48% comes entirely from the DC source. 00:06:40.417 --> 00:06:41.750 align:center line:-1 position:50% size:28% Let me illustrate this. 00:06:41.750 --> 00:06:46.375 align:center line:-1 position:50% size:58% First, we have to note that the starting point at the current source is the DC offset, 00:06:46.375 --> 00:06:49.000 align:center line:-1 position:50% size:52% which is provided by the power supply. 00:06:49.000 --> 00:06:52.792 align:center line:-1 position:50% size:65% Let's see what happens when the input sinusoidal voltage goes negative. 00:06:52.792 --> 00:06:56.083 align:center line:-1 position:50% size:64% Well, that causes the current through the device to also go negative. 00:06:56.083 --> 00:06:59.458 align:center line:-1 position:50% size:45% Depending on the bias current, this can go all the way down to 0. 00:06:59.458 --> 00:07:02.375 align:center line:-1 position:50% size:53% Now, since less current is getting pulled into the current source, 00:07:02.375 --> 00:07:07.708 align:center line:-1 position:50% size:48% instead, it flows in an AC sense from the power supply into the load. 00:07:07.708 --> 00:07:10.042 align:center line:-1 position:50% size:63% This causes the current in the load to increase. 00:07:10.042 --> 00:07:15.083 align:center line:-1 position:50% size:58% Since the load is a resistor, that means that the voltage in the load increases too. 00:07:15.083 --> 00:07:16.625 align:center line:-1 position:50% size:53% When the voltage in the load increases, 00:07:16.625 --> 00:07:21.333 align:center line:-1 position:50% size:61% the voltage across the device's current source also increases. 00:07:21.333 --> 00:07:22.833 align:center line:-1 position:50% size:42% If the input signal goes positive, 00:07:22.833 --> 00:07:26.042 align:center line:-1 position:50% size:48% then the current source draws more current from the supply. 00:07:26.042 --> 00:07:29.875 align:center line:-1 position:50% size:64% This is more current than the supply is providing in a DC sense. 00:07:29.875 --> 00:07:31.542 align:center line:-1 position:50% size:57% Where does that extra current come from? 00:07:31.542 --> 00:07:34.708 align:center line:-1 position:50% size:65% Well, it gets pulled through the load from ground. 00:07:34.708 --> 00:07:39.542 align:center line:-1 position:50% size:57% This decreases the voltage at the load, which decreases the voltage at the device. 00:07:39.542 --> 00:07:43.542 align:center line:-1 position:50% size:49% Now, keep in mind that there's also a DC voltage bias on the device too. 00:07:43.542 --> 00:07:46.500 align:center line:-1 position:50% size:44% The voltage here might be going from the DC value down to 0. 00:07:46.500 --> 00:07:50.833 align:center line:-1 position:50% size:61% When I say they're coupled, I really mean they're coupled in an AC sense. 00:07:50.833 --> 00:07:53.625 align:center line:-1 position:50% size:68% This is fundamentally how a power amplifier works. 00:07:53.625 --> 00:07:55.833 align:center line:-1 position:50% size:65% There's one more thing that we need to consider. 00:07:55.833 --> 00:08:00.542 align:center line:-1 position:50% size:60% Since there's a DC offset across the device, power is not just being dissipated in the load, 00:08:00.542 --> 00:08:05.083 align:center line:-1 position:50% size:47% it's also being dissipated in the current source of the device. 00:08:05.083 --> 00:08:06.958 align:center line:-1 position:50% size:41% Let's take a closer look at this. 00:08:06.958 --> 00:08:09.917 align:center line:-1 position:50% size:58% Here, I have voltage and current sinusoids. 00:08:09.917 --> 00:08:12.208 align:center line:-1 position:50% size:56% These are offset by DC bias components. 00:08:12.208 --> 00:08:15.458 align:center line:-1 position:50% size:36% Here's the DC voltage, and here's the DC current. 00:08:15.458 --> 00:08:21.000 align:center line:-1 position:50% size:64% These sinusoids are swinging from a peak of twice the DC value to a minimum of 0. 00:08:21.000 --> 00:08:23.500 align:center line:-1 position:50% size:44% We can also show the DC power directly on this plot. 00:08:23.500 --> 00:08:26.125 align:center line:-1 position:50% size:45% Obviously, it's constant over time. 00:08:26.125 --> 00:08:29.500 align:center line:-1 position:50% size:59% Since these waveforms are always positive, to find the dissipated power, 00:08:29.500 --> 00:08:32.500 align:center line:-1 position:50% size:57% we simply multiply the waveforms together and integrate. 00:08:32.500 --> 00:08:34.000 align:center line:-1 position:50% size:35% The result will be positive. 00:08:34.000 --> 00:08:36.542 align:center line:-1 position:50% size:59% This represents the portion of the DC power 00:08:36.542 --> 00:08:40.917 align:center line:-1 position:50% size:52% which is dissipated inside of the device at the current source. 00:08:40.917 --> 00:08:44.792 align:center line:-1 position:50% size:45% Now, if we remove the DC offsets from the RF waveforms, 00:08:44.792 --> 00:08:47.042 align:center line:-1 position:50% size:62% it's then easy to calculate the power generated 00:08:47.042 --> 00:08:50.958 align:center line:-1 position:50% size:66% because we can just multiply the signals together, and the result should be negative. 00:08:50.958 --> 00:08:52.542 align:center line:-1 position:50% size:44% Now, since energy is conserved, 00:08:52.542 --> 00:08:56.167 align:center line:-1 position:50% size:45% it also shouldn't be surprising that the area of the dissipated power, 00:08:56.167 --> 00:08:58.042 align:center line:-1 position:50% size:63% combined with the area of the generated power 00:08:58.042 --> 00:09:01.833 align:center line:-1 position:50% size:44% is exactly equal to the DC power put in by the supply. 00:09:01.833 --> 00:09:06.333 align:center line:-1 position:50% size:56% What I'm showing here are the waveforms for what's called a class A power amplifier. 00:09:06.333 --> 00:09:08.083 align:center line:-1 position:50% size:42% I just proved for this type of PA, 00:09:08.083 --> 00:09:12.083 align:center line:-1 position:50% size:41% at best, half of the DC power will be converted to RF power. 00:09:12.083 --> 00:09:16.458 align:center line:-1 position:50% size:58% As you might guess, this amplifier will be, at most, 50% efficient. 00:09:16.458 --> 00:09:21.042 align:center line:-1 position:50% size:61% The concept of efficiency for power amplifiers should now be quite clear. 00:09:21.042 --> 00:09:24.458 align:center line:-1 position:50% size:50% At the output, the efficiency is defined as the generated power 00:09:24.458 --> 00:09:27.375 align:center line:-1 position:50% size:49% over the sum of the generated and dissipated power. 00:09:27.375 --> 00:09:30.625 align:center line:-1 position:50% size:53% Or, in other words, the generated power over the DC power. 00:09:30.625 --> 00:09:34.167 align:center line:-1 position:50% size:55% This is often expressed as a percentage. 00:09:34.167 --> 00:09:38.667 align:center line:-1 position:50% size:56% Using the interactive waveform generator, which you can also download, 00:09:38.667 --> 00:09:42.333 align:center line:-1 position:50% size:54% it's possible to see what different types of waveform configurations will give you, 00:09:42.333 --> 00:09:46.375 align:center line:-1 position:50% size:43% in terms of generated power, dissipated power, and efficiency. 00:09:46.375 --> 00:09:48.333 align:center line:-1 position:50% size:62% It even tells you if a waveform is non-physical. 00:09:48.333 --> 00:09:50.417 align:center line:-1 position:50% size:46% In other words, it tells you if you have a waveform 00:09:50.417 --> 00:09:53.125 align:center line:-1 position:50% size:69% where the generated power exceeds the DC power. 00:09:53.125 --> 00:09:57.667 align:center line:-1 position:50% size:39% This is a waveform that you can't build in the lab. 00:09:57.667 --> 00:10:00.917 align:center line:-1 position:50% size:38% Finally, let's talk about how to pick the load resistor. 00:10:00.917 --> 00:10:04.167 align:center line:-1 position:50% size:44% To start, I'll take the configuration that I showed earlier, 00:10:04.167 --> 00:10:08.292 align:center line:-1 position:50% size:54% with current source and a resistor, and I'll sweep the current in a DC sense. 00:10:08.292 --> 00:10:13.542 align:center line:-1 position:50% size:59% Then, I'll plot the current versus the voltage, current on the Y-axis, voltage on the X-axis. 00:10:13.542 --> 00:10:15.875 align:center line:-1 position:50% size:49% I get a simple negatively sloped line. 00:10:15.875 --> 00:10:19.083 align:center line:-1 position:50% size:47% Now, the magnitude of the slope is equal to one over the resistance, 00:10:19.083 --> 00:10:23.583 align:center line:-1 position:50% size:62% since the slope is Y/X, or current over voltage. 00:10:23.583 --> 00:10:26.083 align:center line:-1 position:50% size:66% Let's expand this simple analogy to a real device. 00:10:26.083 --> 00:10:28.083 align:center line:-1 position:50% size:61% For example, here, I have a CMOS transistor, 00:10:28.083 --> 00:10:32.750 align:center line:-1 position:50% size:55% which is similar to the small-signal model that I showed earlier. 00:10:32.750 --> 00:10:36.875 align:center line:-1 position:50% size:56% If we take a look at current versus voltage at the drain node of this transistor, 00:10:36.875 --> 00:10:37.917 align:center line:-1 position:50% size:34% we get a family of curves, 00:10:37.917 --> 00:10:42.000 align:center line:-1 position:50% size:55% where each curve is the output response for a different input voltage. 00:10:42.000 --> 00:10:45.500 align:center line:-1 position:50% size:50% To make this circuit operate correctly, we need to bias the transistor. 00:10:45.500 --> 00:10:49.000 align:center line:-1 position:50% size:62% Let's pick a DC bias point in the middle of the voltage and current range. 00:10:49.000 --> 00:10:53.292 align:center line:-1 position:50% size:42% Something like 250 mA and 5 V will work for this case. 00:10:53.292 --> 00:10:55.250 align:center line:-1 position:50% size:52% Now, if I go back to my current source, 00:10:55.250 --> 00:10:58.375 align:center line:-1 position:50% size:42% and I add this fixed bias current into my current source 00:10:58.375 --> 00:11:02.667 align:center line:-1 position:50% size:66% and redo the DC sweep, you can see that the scales on the curve change. 00:11:02.667 --> 00:11:07.458 align:center line:-1 position:50% size:55% Now, the line, instead of being centered around a negative point, is centered at 0. 00:11:07.458 --> 00:11:10.917 align:center line:-1 position:50% size:44% 0, in this case, is the bias point of the transistor. 00:11:10.917 --> 00:11:12.917 align:center line:-1 position:50% size:55% We can just superimpose the two curves. 00:11:12.917 --> 00:11:14.958 align:center line:-1 position:50% size:48% This is what is called a loadline plot. 00:11:14.958 --> 00:11:18.042 align:center line:-1 position:50% size:51% It's very commonly used in PA design. 00:11:18.042 --> 00:11:21.875 align:center line:-1 position:50% size:55% The load resistor is really setting the ratio between the peak-to-peak voltage 00:11:21.875 --> 00:11:24.042 align:center line:-1 position:50% size:40% and the peak-to-peak current. 00:11:24.042 --> 00:11:27.292 align:center line:-1 position:50% size:56% It's important to keep in mind that this is also constrained by the device. 00:11:27.292 --> 00:11:30.083 align:center line:-1 position:50% size:48% For example, there's a knee voltage in practical devices 00:11:30.083 --> 00:11:33.625 align:center line:-1 position:50% size:51% which prevents the voltage waveforms from swinging all the way to 0. 00:11:33.625 --> 00:11:37.792 align:center line:-1 position:50% size:67% This needs to be considered in the design as well. 00:11:37.792 --> 00:11:40.833 align:center line:-1 position:50% size:47% If you want to learn more about the material that I discussed today, 00:11:40.833 --> 00:11:44.000 align:center line:-1 position:50% size:49% I'm making this Workspace available for you to download. 00:11:44.000 --> 00:11:45.833 align:center line:-1 position:50% size:54% It covers everything I talked about today, 00:11:45.833 --> 00:11:48.833 align:center line:-1 position:50% size:50% from calculating power directly from time domain waveforms, 00:11:48.833 --> 00:11:50.542 align:center line:-1 position:50% size:29% to drawing a loadline. 00:11:50.542 --> 00:11:52.875 align:center line:-1 position:50% size:66% There's some more advanced capability here too. 00:11:52.875 --> 00:11:55.792 align:center line:-1 position:50% size:38% For example, you can set the bias current up to rectify, 00:11:55.792 --> 00:11:59.500 align:center line:-1 position:50% size:58% which will allow you to explore waveforms for more advanced classes of PA operation, 00:11:59.500 --> 00:12:02.833 align:center line:-1 position:50% size:50% like class AB, and see how this improves efficiency. 00:12:02.833 --> 00:12:05.708 align:center line:-1 position:50% size:43% I think it's a great way to master these basic concepts.