10. Amplifiers

10.1. Objectives

  1. Learn how to use a MOSFET as an amplifier
  2. Gain experience designing amplifier bias networks
  3. Review Bode plots
  4. Observe the spectra of different signals

10.2. Required Soft Front Panels (SFPs)

  1. Digital Multimeter
  2. Function Generator (FGEN)
  3. Scope
  4. Bode Analyzer
  5. Dynamic Signal Analyzer

10.3. Required Components

  1. ZVN4306 MOSFET
  2. 1 k\Omega resistor
  3. three 150 k\Omega resistors
  4. 3 numbers of 1 \mu F capacitor
  5. three 20 k\Omega resistors
  6. 10 k\Omega resistors
  7. two 2.2 k\Omega resistors
  8. 220 \Omega resistor

10.4. Overview

10.4.1. Fundamentals of MOS Transistor Amplifiers

Consider a MOSFET with a resistive load at the drain, like the one shown in figure 1. This circuit is very similar to the resistor-load inverter.

ideal-amplifier

Figure 1: Ideal MOSFET amplifier.

A change in Vgs causes a change in IDS, which then causes a change in the output voltage.

So first order theory gives us \Delta V_{out} = \Delta I_{ds} * R_{load}.

Voltage gain is thus:

(1)A_{v}  = \frac{\Delta V_{out}}{\Delta V_{gs}} = \frac{\Delta I_{ds}}{\Delta V_{gs}} * R_{load}

\Delta I_{ds} / \Delta V_{gs} is called the transconductance gm.

This equation, however, assumes very small AC input voltage, so that the output voltage change is still small.

So if we make the small signal voltage gain 100, and we set the AC input voltage amplitude to 1mV, then the AC output voltage amplitude will be 100 * 1mV = 0.1V.

10.4.2. Output Voltage Swing - Maximizing It with Bias Point Design

Now if V_{in} = \Delta V_{gs} = 2V, \Delta V_{out} is not going to have an amplitude of 2V * 100 = 200V. Rather V_{out} will saturate as we have demonstrated with a real amplifier.

When V_{gs} is below threshold, the transistor cuts off. Thus, the highest V_{out} possible is V_{dd} - 0 * R_{Load} = V_{dd}.

When V_{gs} is very high, the current will increase, and hence pull down V_{out} = V_{dd} - I_{ds} * R.

For an ideal transistor with an ideal knee voltage or with a drain saturation voltage V_{dsat}=0V, the best V_{out} low we can achieve occurs when I_{ds} * R = V_{dd}, and V_{out} decreases to zero.

If we further assume that the transistor I_{ds} - V_{gs} is linear, we find that a maximum output voltage swing of V_{dd} / 2 can be obtained if we choose a DC V_{ds} equal to V_{ds,dc} = V_{dd} / 2, as shown in figure 2.

load-line

Figure 2: Ideal load line.

The load resistance R_{load} is simply the ratio of the voltage swing (V_{ds,dc} or V_{dd}/2) to current swing (I_{ds,dc}):

(2)R_{load} = \frac{V_{ds,dc}}{I_{ds,dc}} = \frac{V_{dd}}{(2 * I_{ds,dc})}

Well, real MOSFETs are not so ideal, as we have seen from measured I_{ds}-V_{ds} curves. The I_{ds}-V_{ds} relation is not exactly linear but not too far off, either. The knee voltage, or V_{dsat}, at which saturation occurs can be quite a bit above 0V, however. That fact can be taken into account by setting aside voltage room for the transistor to saturate. The consequence is basically that the lowest V_{out} will not be zero volts.

10.4.3. Stabilizing DC Bias Point with a Resistor at Source

We have seen that the output voltage and current swing have a lot to do with the DC I_{ds} and DC V_{ds}, which we denote as I_{ds,dc} and V_{ds,dc}. Together they are called the DC bias point.

It is necessary to stabilize the DC bias point against fluctuations of V_{dd}, temperature, K factor, or even transistor threshold voltage.

Take an increase in V_{dd} for example. It directly translates into a V_{gs,dc} increase, which then increases I_{ds,dc}.

With a resistor between source and ground, as shown in figure 3, an increase of V_{dd} increases V_{g}, which then increases I_{ds}.

amplifier-drawing

Figure 3: MOSFET amplifier with feedback resistor.

The I_{ds} increase, however, increases V_{s} = I_{ds} * R_{s}. Consequently, the resulting V_{gs} increase is less than the original V_{g} increase from the V_{dd} increase, simply because V_{gs} = V_{g} - V_{s}.

The R_{s} resistor is thus said to act as a negative feedback, as it negatively affects the increase of I_{ds}.

10.4.4. AC Operation Consideration of Feedback

For an AC signal, we do not necessarily want the large negative feedback.

Assume we want all of the AC input voltage to appear across V_{gs}, without any drop over R_{s}. We can just add a large enough capacitor across R_{s}, so that R_{s} is shorted out by the capacitor, as shown in figure 3.

10.4.5. Design Procedure

  1. Choose a reasonable V_{s} for stability of dc bias, this sets R_{s}=V_{s}/I_{ds,dc}.
  2. Find V_{gs} necessary to produce the I_{ds,dc} given.
  3. In simulation, just connect the drain and gate together for saturation operation, force a current of I_{ds,dc}, and read the voltage value.
  4. In the lab you can run a 2-wire analyzer measurement in the same way that you found the threshold voltage from a given threshold current.
  5. Find V_{g} = V_{gs} + V_{s}.
  6. Find R1 and R2 that will give the desired V_{g,dc}.
  7. Approximately set V_{ds,dc} = (V_{dd}-V_{s})/2.
  8. Determine R_{load} = V_{ds,dc} / I_{ds,dc}.

We can consider the finite V_{dsat} in design and simulation. For first order design, the above simplification works just fine, and greatly simplifies the design.

10.4.6. Vs choice Tradeoffs

A larger V_{s} means more feedback, and gives a more stable dc bias point against V_{dd}, temperature, transistor V_{t}, and transistor K variation. However, more V_{s} means less voltage room to work with. Remember that V_{dd} - V_{s} is the available voltage room to work with. Furthermore, for real transistors, we have to choose V_{ds,dc} to be approximately above V_{gs,dc}-V_{t} to be in the saturation region.

10.4.7. R1, R2 choice

R1//R2 (R1 in parallel with R2) will be the input impedance seen by the ac voltage source (shown in figure 4).

amplifier-drawing-with-capacitors

Figure 4: MOSFET amplifier with feedback resistor and DC blocking capacitors.

Normally we want R1 // R2 to be large, say around 100 k\Omega or more.

Generally, we do not want R1//R2 to be small, as it will place too much of a load on the AC source. A small R_{in} means a large input current requirement, or a “heavy” load. An extreme example would be a short circuit of a load to a source.

10.4.8. DC Blocking Capacitors

Normally, when we think of an AC signal, it is centered about zero volts. Think about the signal driving your speakers. However, if the output of the amplifier is taken directly from the drain, it will have a considerable DC bias. The solution is the addition of a capacitor at the output, as shown in figure 4. This capacitor will allow the amplified signal to pass, but not the DC bias. That is why they are called DC blocking capacitors, or alternatively, AC coupling capacitors.

A capacitor is also needed at the input. Otherwise, the gate voltage might be changed by the device that is driving it. Worse, the device connected to the amplifier might be damaged by the gate voltage. Think about connecting the line out jack of a CD player to a stereo.

10.4.9. BJT Amplifiers

The schematic of a bipolar transistor amplifier using a 4R bias circuit is shown below in figure 5.

4R bias amplifier schematic

Figure 5: Bipolar transistor amplifier schematic.

We can immediately recognize the 4R biasing circuit used. Note that we have two Re’s, Re1 and Re2, Re1 is for negative feedback in “ac” signal. Re2 is for negative feedback in DC bias. Exactly how to choose (I_{C}, V_{CE}) will take more discussions which will be covered in Analog Electronics. For now, let us consider that we have been given a (I_{C}, V_{CE}) bias point. We have designed a biasing circuit to produce the required (I_{C}, V_{CE}) using a Si bipolar transistor, 2N3904 in this experiment.

We have added 3 capacitors that are going to block DC and pass AC. Of course, each capacitor’s impedance depends on frequency. A photo of a bipolar transistor amplifier using 4R bias is shown below in figure 6.

4R bias amplifier photo

Figure 6: Bipolar transistor amplifier on ELVIS breadboard.

10.5. Pre lab

  1. Find the gate-source voltage necessary for a 1mA drain current. You may find this multisim file helpful: download. It contains the correct model for the MOSFET used in the lab.

  2. Design a 4 resistor biasing network for a MOSFET with a drain current of 1mA, 1v source voltage, and an input equivalent resistance of 110 k\Omega. The input resistance is defined as R1||R2. V_{dd} is 5v. A sample circuit is shown in figure 7.

    sample-circuit

    Figure 7: Sample MOSFET bias network.

  3. Verify the DC operating point of your bias network with Multisim. Measure V_{d}, V_{s}, and V_{gs}. Use the ELEC2210_ZVN4306A (used in prelab step 1) as the MOSFET.

  4. Add 1 \mu F capacitors to your circuit, as shown in figure 8, and then simulate your amplifier using Multisim. Select AC Analysis and sweep from 10Hz to 5MHz. Plot Output/Input.

In order to make your graph show up better when printed (and save toner), use a white background. From the grapher view menu bar select Graph > Black and White Colors.

10.6. Lab Exercises

10.6.1. MOSFET Amplifier Biasing Network

  1. Construct a biasing network for a ZVN4306 using the resistor values calculated in the prelab,as shown in figure 7. Use 5v for V_{dd}.

    Use 190 k\Omega resistor(one 150 k\Omega resistor plus two 20 k\Omega resistor) as R2, 300 k\Omega resistor (two 150 k\Omega resistors) as R1, and 2.2 k\Omega resistor as Rd.

  2. Measure the drain voltage, source voltage, and V_{gs} using DMM.

What to do in lab report

Compare measured voltages with expected values.

10.6.2. MOSFET Amplifier

  1. Add three capacitors to your circuit, as shown in figure 8.

    amplifier

    Figure 8: MOSFET Amplifier.

  2. Connect the function generator to the input of the amplifier. Select a 5kHz sine wave, 0.05vpp.

  3. Connect the input of the amplifier to AI0 and connect the output to AI1, as shown in figure 9.

    scope

    Figure 9: Oscilloscope settings.

  4. Take screenshots of the output and input waveforms at several frequencies: 500Hz, 2kHz, 5kHz, 20kHz for calculating ac voltage gain later in lab report. Use the formula Gain = \frac{V_{pp,out}}{V_{pp,in}}. Only absolute value is required, but you should notice that transistor is naturally inverting in this amplifier configuration. Select a scale large enough that allows accurate amplitude measurements.

  5. Make measurements and take screenshots so that you can later calculate the ac voltage gain’s absolute value for the following input amplitudes at 5kHz: .1vpp, .2vpp, .4vpp, .7vpp, 1vpp, 1.3vpp.

    Note

    Keep in mind that as you adjust the input amplitude, your scope settings will need to be adjusted accordingly. The entire waveform must be visible on the scope display in order to make accurate measurements.

  6. Use AI1 to measure the drain and source voltages for an input of 5kHz, 1.3vpp. See figure 10 below for an example of the drain voltage.

    scope vd

    Figure 10: Drain voltage of clipping amplifier.

    Also observe the drain and source voltage waveforms in the Oscilloscope by connecting AI0 to source and AI1 to drain, as shown in figure 11. Use the exact Oscilloscope settings as shown in the plot, and take a screenshot.

    What are the maximum and minimum values of Vd?

    scope vd vs

    Figure 11: Source and drain voltage of clipping amplifier.

What to do in lab report

Show screenshots and calculate gain for all measurements.

Plot measured gain as a function of Vin.

Show screenshots of Vd and Vs. Explain what you see.

10.6.3. Spectrum Analyzer

  1. Open the Dynamic Signal Analyzer. Set the source channel to AI1.

  2. Set the function generator to produce a 5kHz sine wave at .05vpp. Take a screenshot of the output signal spectrum, similar to the one in figure 12.

    spectrum analyzer

    Figure 12: Spectrum analyzer.

  3. Increase the amplitude until the output is clipping near both peak and valley, similar to the amplitude in figure 13. Take a screenshot of the output spectrum.

    spectrum analyzer clipping

    Figure 13: Output is clipping.

  4. Experiment with other types of waveforms, amplitudes, frequency sweeps, etc.

What to do in lab report

Compare the sinusoidal output spectrum to the spectrum of the waveform that is clipping. Explain why they are different. Include anything else you found interesting.

10.6.4. Bode Plot

  1. Open the Bode Analyzer. Set the start frequency to 100Hz and set the Stop frequency to 20kHz. Use a peak amplitude of .05, as shown in figure 14. Take a screenshot.

    Bode analyzer

    Figure 14: Bode analyzer.

    This plot doesn’t show a complete gain vs frequency characteristic, due to the limit of myDAQ. Below is a plot measured using ELVIS board, showing the change of gain, when frequency increases from 10Hz to 5MHz.

    Bode analyzer elvis

    Figure 15: Complete gain vs frequency in Elvis.

What to do in lab report

Compare the measured frequency response with the simulated results from pre lab.

10.6.5. BJT Amplifier

  1. Construct the BJT amplifier shown below in figure 16. Notice that the circuit is exactly like the MOS amplifier with the exception that the MOS transistor is replaced by a BJT 2N3904 and different resistors are used.

    When building the circuit, use 2.2 k\Omega resistors to replace 2.67 k\Omega resistor and 2.42 k\Omega resistor. Use one 10 k\Omega resistor and one 20 k\Omega resistor in series to get the 30 k\Omega resistor, and use two 20 k\Omega resistor to get the 40 k\Omega resistor.

    Re1 in the schematic is for AC feedback. Re2 acts as DC feedback to make DC bias points stable. figure 16 shows the schematic without the AC feedback.

    bjt-amp-schematic

    Figure 16: BJT amplifier schematic.

  2. Set the function generator to produce a 10kHz, 0.02Vpp sine wave, as shown in figure 17.

    bjt-amp-002

    Figure 17: BJT amplifier output without AC feedback at 0.02vpp.

    Take a screenshot of the waveform, and calculate the gain. Then set the function generator to produce a 10kHz, 0.06Vpp sine wave, as shown in figure 18.

    bjt-amp-s1

    Figure 18: BJT amplifier output without AC feedback at 0.06vpp.

    Take a screenshot and calculate the gain. The output already has distortion at the low input without the AC feedback, but the gain is high.

    Measure the collector and emitter voltage using Oscilloscope, as shown in figure 19. Set the FGEN to 5kHz, 1.3vpp. Use the exact Oscilloscope settings as shown below.

    bjt-amp-largevpp

    Figure 19: Ve and Vc without AC feedback.

    Take a screenshot. What’s the relation between Vc and Ve? Also compare it with the screenshot you get from MOSFET amplifier Vd and Vs in step 10.6.2, what conclusion can you get?

  3. Add an AC feedback, rewire the circuit as shown in figure 20.

bjt-amp-s2

Figure 20: BJT amplifier schematic with AC feedback.

Set the FGEN to 10kHz, 0.02vpp, you will get a plot similar to figure 21. Take a screenshot and calculate its gain.

bjt-amp-002ac

Figure 21: BJT amplifier output with AC feedback at 0.02vpp.

Then set the FGEN to 10kHz, 0.06vpp, as shown in figure 22. Take a screenshot and calculate its gain.
bjt-amp-s3

Figure 22: BJT amplifier output with AC feedback.

The distortion disappears at this time. However, the gain is reduced.

Comparing the gain and linearity of the output of both schematic, we can see there is a representative tradeoff in amplifier design.

Keep this circuit with the AC feedback and use it in the following steps.

  1. Measure Vc and Ve of the BJT amplifier using the scope at 5kHz and 1.3vpp sine wave input, use the same settings as in figure 19. Compare the waveform with the Vc and Ve get from no AC feedback schematic, do you see any difference?
  2. Use the dynamic signal analyzer to measure the output spectrum for a 5kHz, 0.05vpp sine wave input. Be sure to set the source to AI1. Take a screenshot of the output signal spectrum, similar to the one in figure 12.
  3. Open the Bode Analyzer. Set the start frequency to 20Hz and set the Stop frequency to 20kHz. Use a peak amplitude of .05. Take a screenshot.

What to do in lab report

Show screenshots. Compare the output spectrum to that of the MOSFET amplifier.

10.6.6. Clean up

Please place components back in the correct drawer.

Thank you for keeping our lab clean and organized.

Feedback

You are encouraged to write down your experience with this lab along with any feedback or suggestions.

You can also document mistakes or missteps that occurred, e.g.

  • I could not find the correct scope inputs, or
  • the Bode Analyzer confused me,

Such information will be used to improve this and future labs and your experience will help future students.