Welcome back to Electronics, this is Dr. Robinson. In this lesson, we're going to look at the common source amplifier, and in particular we're going to look at the DC Analysis of this amplifier. In your previous lesson, we examined MOSFET characteristic curves and biasing and our objectives for this lesson are to introduce the common source amplifier and to analyze the common source amplifier at dc. Now you can think of this lesson as a practical application for a MOSFET transistor. What we want to do is look at a circuit that can be used to implement a gain stage or a gain block in a system. So at the system level, we can consider a gain block to be, let me draw the block. And label with its gain A. So to the circuit we apply an input voltage, Vin. And we have an output voltage from this block, Vout. Which is equal to the gain A times the input voltage. Now, to actually implement a gain block that has this functionality, we have to build a circuit. And you know one way of doing this. So, for example, we could use a non-inverting op-amp amplifier or an inverting op-amp amplifier to implement this functionality. We designed the circuit so that they have a gain A. But, in this lesson, what we're going to do is look at another way to do this. We're going to look at how you can use a discreet MOSFET transistor to implement this gain block. Now, there are numerous single MOSFET circuits that can implement this gain functionality, but during this lesson we're going to look at one particular type called the common source amplifier or CS amplifier. Now as we go through this lesson we should keep in mind the relationship between a MOSFET's biasing, or its quiescent point, and its behavior. Remember in the previous lesson, we looked at how by changing the external voltages and currents of the MOSFET, we can change its behavior. And in particular, we can change its region of operation. Now you may also remember that for MOSFET to operate as an amplifier, we must bias the transistor in its saturation region. Keep in mind as we go through the lesson that we can change the characteristics of this amplifier by changing externally the DC bias. In the following we're first going to introduce the common source amplifier circuit, and then we're going to spend some time looking in particular at the design equations necessary to buy us the transistor in its saturation region. So, let's take a look at the circuit. Now, in the circuit, VDD is a DC voltage, a positive DC voltage, and VSS is a negative DC voltage. These voltages, in combination with R1, R2, RD and RS set the cue point of the MOSFET. Now these components along with R3 and the capacitor values, control the AC performance of this amplifier or effect the gain of this circuit. Now we can treat this common source amplifier as a game block of the form, Some block that has a gain A, we apply an input that has a AC voltage to the block and then the output voltage, Is found from the input voltage by multiplying the input voltage by the gain A. A times VN. But before we can treat this circuit as this block, we must know the operating point of the transistor. Because its operating point affects its gain. Now remember that a capacitor's impedance Z sub c can be written as 1 over J Omega C. So at very low frequencies at DC voltages and DC currents the voltages and currents that set the operating point of the MOSFET. The impedance of the capacitor is very large. So as omega goes to zero, in other words the quantities go to DC quantities, this impedance does an open circuit. So, in determining the Q point for this transistor, which determines this circuit's gain characteristics, we can treat all of the capacitors in the circuit as open circuits or large impedance. So here I've redrawn the previous circuit with all of the capacitors made open circuits. So we can analyze the DC performance of the common source amplifier or determine it's cue point or quiescent point. Now because of the structure of our MOSFET, we know that the gate current into the MOSFET is zero. IG, the gate current, is equal to zero and we also know that ID, the drain current, is equal to IS, the source current. Or in other words, the current going into the drain all comes out of the source, so that both the drain current and the source current are equal to each other. Now what we want to determine is the Q point of this transistor. In other words, what is it's drain current and what are the drain voltage, the gate voltage, and the source voltage for this transistor. Now we can write an equation for the gate voltage in terms of R1, R2, VDD and VSS. We know there's no current into the gate here, so we could, one way of doing this would be to use superposition between VDD and VSS to solve for the voltage here at the gate. Or we could use Ohm's Law to determine the current through these two resistors and then solve for the voltage here by adding the drop across R2 to the voltage VSS. So in other words we can solve for this current here, I, by Vdd minus Vss divided by R1+R2. We take that current I, and multiply by the resistor R2 to get the voltage drop across R2. And then we add that drop to VSS to find VG, the gate voltage. So we can say that VG is equal to VDD R2+VSS R1 divided by R1 + R2. So here we have an equation that relates or lets us calculate the gate voltage in terms of the passive component values and the DC power supply values. Now we can also write a loop equation from the gate voltage to the voltage VSS. So what I'm going to do is start at this known voltage VG, work my way around this loop to this known voltage VSS, which is going to give us an equation in the gate to source voltage, VGS. So let me write, VG, the voltage here, minus the gate to source voltage, the voltage from the source to the gate, minus VGS, would get us to here, then minus the drop across RS. Must be equal to the voltage at this node VSS. Now we know that ID = IS. And at this transistor is operating as an amplifier, we know it's operating in its saturation region, where ID = K(VGS- VTO) squared. Or, we can solve this equation for VGS. VGS is equal to the square root of ID over K plus VTO. Then we can substitute this expression for VGS that we obtained from knowing that the MOSFET is operating in its saturation region into this loop equation to give us a single equation in known voltages and ID. So this results, after substitution of this equation into this equation, a quadratic equation, in terms of the square root of ID. And we can then solve that equation for ID. Now because it's a quadratic equation there'll be two solutions. But it will turn out that one of the two solutions places the MOSFET in a region of operation that is not allowed for it acting as an amplifier. In other words, one value of ID would place the transistor in it's cut-off region, while the other value for ID would place the transistor in it's saturation region, the region it must in be in for it to act as an amplifier. Here I've rewritten two of the equations we obtained on the previous slide. The equation for the gate voltage, the DC gate voltage in terms of the DC voltage sources and the circuit element values. And this equation for VGS, that results from the transistor operating in its saturation region. I've also solved the quadratic equation for ID to get this expression. And I kept only the solution, the results in the transistor operating in its saturation region. And to simplify this expressions somewhat I defined a voltage V1. That's given by VG minus VSS minus VTO. So this value is calculated, then placed into this expression, along with the circuit element values and MOSFET parameters to calculate the drain current through the MOSFET. Now I've written two additional equations, that allow us to solve for the node voltage at the drain, or the drain voltage. From the equation, you can see how it's obtained. The voltage at the drain of the MOSFET, VD, is equal to the voltage here VDD, minus the voltage drop across RD. And that voltage drop, by Ohm's law, would be equal to IDRD. So the VDD, a voltage we know, minus a voltage drop across the resister, gets us to the node voltage VD, as shown by this equation. And then similarly the voltage at the source of the MOSFET, VS, we can find it by starting at VSS, this known DC voltage, and then going up by one voltage drop across RS. So VSS plus this voltage drop gives us an expression for the source voltage of the MOSFET. Now, these equations taken together allow us to solve for the operating point, the DC operating point of a common source amplifier. So in summary, during this lesson we introduced the common source or CS amplifier and we performed a dc analysis to derive the dc design equations for this amplifier. In the next lesson we will continue our look at the common source amplifier. We'll perform an AC analysis. So thank you and until next time.