So welcome back to Electronics. This is Dr. Robinson. In this lesson we're going to look at what are called Voltage Transfer Characteristics. In your previous lessons, we introduced half-wave and full-wave rectifiers, and we analyzed example circuits that were used to implement these types of rectifiers. In today's lesson we're going to introduce voltage transfer characteristics. We're then going to use VTCs to determine a circuit's output for a given input. And we're also going to, from given input and output plots, see if we can determine a circuit's voltage transfer characteristic. A voltage transfer characteristic can be thought of as a graphical description of the behavior of a nonlinear circuit. It's simply a plot of the output voltage versus the input voltage for a circuit. And let's look at how the voltage transfer characteristic can be obtained from an equation. If you remember this equation, we've found it when we analyzed the positive half-wave rectifier circuit in a previous lesson. For a positive half-wave rectifier, the output is equal to the input, when the input is positive, and the output is equal to 0 when the input is negative. Here I have two axes. An output voltage axis and an input voltage axis. For the region on this graph, where the input voltage is positive, to the right of the V-out axis. We know that the output must be equal to the input. So I've drawn a line with the slope of 1 volt per volt. When the input voltage is 1, the output voltage is 1. When the input voltage is 2, the output voltage is 2. Now, in the region of the graph where the input voltage is negative, we know that the output voltage must be equal to 0, so I've drawn a horizontal line here at V-out equals 0 volts. Now, if you remember, the circuit that we analyzed to obtain this equation had a single diode in it. And that diode could be either off or on. So this circuit had two states, as indicated by this equation. One state, one state. Now it's immediately apparent from the voltage transfer characteristic that the circuit has two states. Here is state one, here is state two. And on a voltage transfer characteristic, every corner on the graph indicates a transition between circuit states. Now let's look at an example where we use a voltage transfer characteristic to determine the output of a circuit for a given input. Here's a voltage transfer characteristic that describes the behavior of our circuit. And here's the voltage wave form. Now we can see that when the input voltage waveform is positive, the output voltage is exactly equal to the input voltage. So on this curve where the input voltage is positive, we know the output voltage is exactly equal to the input voltage. So I can draw the output voltage as tracking the input voltage in this region. Now, from the VTC, we see that when the input voltage is negative, the output voltage is obtained by multiplying the input voltage by minus one. So, when the input voltage is -1, the output voltage is 1. When the input voltage is -2 the output voltage is 2. So on our time domain wave form, when the input voltage is negative, we know to obtain the output voltage, we multiply each one of these voltages by -1. In other words we flip this portion of the curve about the x axis. To obtain this curve here. V-in is positive, so the output is exactly equal to the input. V-in is negative, so the output is equal to the input times -1. And we obtain a curve that looks like this. In other words, this is the voltage transfer characteristic for a positive full-wave rectifier. And this v-shaped curve is characteristic of a full-wave rectifier or absolute value circuit. Now let's look at how we can obtain a voltage transfer characteristic for a circuit from given input and output voltage waveforms versus time. On this graph I'm showing both the input voltage and the output voltage. The input voltage is a sinusoidally varying waveform. The output voltage here is shown in red, and it's known as a center clipped sine wave. The center of the sine wave has been clipped to be 0 volts. Now let me draw some marks on this graph to help us better obtain the VTC. Now, we can see that if the input voltage is less than this value of 3 volts, where the input voltage is less than 3 volts, the output is equal to 0. But when the input voltage is greater than this 3 volt threshold, we obtain the put put voltage by subtracting 3 volts from every point on the input wave form. Now, down here, we can see that when the input voltage is between 0 volts and -3 volts, the output voltage is 0. But when the input voltage becomes less than -3 volts, we obtain the output voltage by adding. Three volts to every value on the waveform. So let's go over our voltage transfer characteristic. Remember, this is the V-out axis. And this is the V-in axis. And we know things are happening at a threshold of -3 and plus 3 volts. If we're in the region where our input is between -3 and plus 3 volts, from our voltage versus time graph, we know the output is exactly equal to 0. Now when our voltage is less than -3 volts in this region, we know we obtain the output voltage by adding 3 volts to every value of the input voltage. So I draw a line that represents the equation V-out is equal to V-in plus 3. Now, when the input voltage is greater than 3 volts in this region here, we know we obtain the output but subtracting 3 volts from every one of our input voltages. So I draw a line that represents the equation. V-out is equal to V-in minus 3 volts. So we have slopes here of +1 and here of +1 and our transition points are at -3 volts and +3 volts. So you can see that this circuit immediately from the VTC, has three states. One state, two states, three states. And two corners in the VTC that represent the transition between the states. So a better picture is shown here of the actual VTC obtained from this plot. Now let's look at how we can use a voltage transfer characteristic to aid us in designing a circuit containing diodes and resistors and implements a particular function. Now, the function we're going to look at here is that the output voltage on this axis is equal to the log base 10 of the input voltage shown on this axis. We're going to use this graph to determine the type of circuit we need to build to approximate this curve. Now a simple approximation would be to draw one point here, one point here and draw a straight line between them. Now this approximation requires no diodes to implement, just resistors, but is not a very good approximation. So another possibility would be to divide this curve into, piecewise linear segments. So say we drew one segment here, one segment here, one segment here, and one segment here. Now, these piecewise linear segments form the voltage transfer characteristic for a circuit it could be used to approximate this log base 10 function. So, from this graph we can see the transition points that must occur in the circuit between the states. And we can see that there are one, two, three, four required states in this circuit. So from the graph, we could read off transition point locations. And the required output voltage versus the input voltage relationship for each state. So during this lesson we looked at voltage transfer characteristics and found that they're simply plots of output voltage versus input voltage for a circuit. A big advantage to a voltage transfer characteristic is it allows one to quickly determine the behavior of a nonlinear circuit. And in our next lesson, we're going to look at an application of rectifiers, AC to DC conversion. Thank you, and until next time.