Laboratory 3: Frequency Response of Common Source To be performed during Week 6 (Sept. 29-Oct. 3) and Week 7 (Oct. 6-10) Due Week 9 (Oct. 20-24) 1 Pre-Lab This Pre-Lab should be completed before attending your regular lab section. The Lab TA will need to see your completed Pre-Lab and check it off at the start of the lab session before you can begin taking your measurements. Read Sections 4.9 and 6.4 in the text, which cover the frequency response of the common source amplifier, and Appendix D.5 which discusses the response of single time constant circuits to a square wave. For this lab, we will analyze the frequency response of the common source amplifier shown in Fig. 1. In the following calculations we will determine how we expect the common source amplifier to operate and low, midband, and high frequencies based on the theory covered in the lectures and the text. For all calculations, use the MOSFET parameters given in Table 1 which are representative values for the 2N7000 transistors we will be using in this lab. You may ignore channel length modulation (V A ) for M 2, but you must consider it for M 1. Consider the common source amplifier shown in Fig. 1, where the node numbers are included for the SPICE simulation component. Resistor R sig represents the output impedance of the signal source, and capacitors C GS and C GD have been added to augment the inherent gate-to-source and gate-to-drain capacitances of the 2N7000 transistors. The high frequency poles that would occur from the inherent capacitances of the 2N7000 transistors are in the range of tens of MHz, but the breadboards used in taking measurements will introduce poles in the 1-2 MHz range. Without the added C GS and C GD capacitors, we would be observing the breadboard poles in the laboratory measurements. The inclusion of the C GS and C GD capacitors will lower the transistor poles so that they dominate over the breadboard poles, and your measurements will (hopefully) match better with your hand calcuations and SPICE simulations. In your hand calculations you may neglect the inherent transistor capacitances, and only consider the specified C GS and C GD values. 1. Calculate the midband gain for this circuit. Parameter Value V t 2.1 V µ n C ox (W/L) 180 ma/v 2 V A 50 V Table 1: Approximate NMOS transistor parameters for hand calculations. 1
Figure 1: Common source amplifier schematic for Pre-Lab and SPICE simulations. 2. Assuming that the dominant pole for this circuit occurs at node 2, estimate the upper 3-dB frequency for this circuit using the dominant pole approximation (use Miller s theorem to calculate the effective capacitance of C GD seen at node 2, as on pages 328-330 of the text). 3. Estimate the upper 3-dB frequency for this circuit using the method of Open Circuit Time Constants. 4. Calculate values for C B1 and C B2 to place the low frequency poles introduced by these capacitors at 500 Hz. 2 Simulations Review the SPICE introduction and tutorial on the website if necessary, and then create a.cir file for the circuit shown in Fig. 1. Use the values for C B1 and C B2 that were calculated in the Pre Lab. The model for the transistor is available on the class website, include the text in the file at the start of your.cir file. Transistors are declared with the command X1 2 1 0 2N7000, where X1 is the reference designator, and 2, 1, and 0 are the drain, gate, and source respectively. Number your nodes as indicated to maintain consistency with the rest of the class, and make it easier to debug your circuit. Now run the following simulations: 1. Simulate the DC operating point. The DC node voltages and transistor currents will be output to the.out file if you specify.op in your input file. Record the node voltages of the gate and drain of M1, as well as the drain current of M1. 2
2. Apply a transient sinusoidal source of 10kHz to the input. Run a transient simulation and find and record the largest input voltage that does not result in visible distortion in the output waveform. Using the same simulation with an input voltage less than the maximum value you just determined, find and record the gain at this frequency (this is the midband gain). 3. Apply a 1 Volt AC source to the circuit and run an AC simulation to observe the frequency response (transfer function). Plot the magnitude and phase, and record the midband gain and both 3dB corner frequencies. 4. Configure your input file so that the AC data points get printed to your.out file. You may want to adjust the number of points per decade to make the number of points more manageable. Save this file so that it can be loaded into Matlab and plotted along with your measurement data in the Analysis section of the lab. Include your SPICE input file(s) in an appendix of your lab report. 3 Measurements The parts that will be used to build the common source amplifier are listed in Table 2, and can be obtained from the EE stores (along with bread boards and wiring equipment). We will use 2N7000 N-Channel field effect transistors during this lab (see data sheet at http://www.ece.utah.edu/~ccharles/ece3110/labs/2n7000.pdf). The pinout diagrams of the TO-92 package that we will be using are shown in Fig. 2. MOSFETs must be handled with care to avoid damaging them; try to avoid touching the gate terminal (middle pin) as the static charge on your fingers can be enough to blow the gate capacitor. When you place the MOSFETs in your bread board, take care to get the drain and source oriented properly as these discrete MOSFETs do not have interchangeable sources and drains. If your circuit is not working correctly, double check that you have the correct orientations. (a) (b) Figure 2: (a) TO-92 package pin-out, (b) N-Channel MOSFET. 3
Component Value/Part Number Quantity MOSFET 2N7000 2 Potentiometer 500 Ω 1 Resistor 10 kω 1 Resistor 1 kω 1 Resistor 200 Ω 1 Resistor 50 Ω 1 Capacitor 2.7 nf 1 Capacitor 270 pf 1 Capacitor C B1 1 Capacitor C B2 1 Table 2: Parts list. Build the circuit shown in Fig. 3. During this experiment, you will be making measurements higher frequencies, where the parasitic capacitance of your breadboard, wires, and the terminals of your discrete components can cause additional poles to appear in your circuit s measured transfer function. To minimize this effect, use the shortest possible wires and clip the terminal wires of your components to be as short as possible. Also, be sure the polarized electrolytic capacitors are connected with the proper polarity. 1. Adjust the 500 Ω potentiometer until I ref (as shown in Fig. 3) is 20 ma. 2. With no AC signal applied to the circuit, measure and record the DC voltages at the gate and drain of M1, as well as the drain current of M1. 3. Apply a small sinusoidal voltage (about 200 mvpp) to the input at a frequency of 10 khz. Use a 10X scope probe to avoid unnecessary loading of the amplifier output. Observe the amplifier output and, if necessary, reduce the magnitude of the input until the output shows no distortion. Record the input and output signal amplitudes, and use these to calculate the midband gain of the amplifier. 4. To get an idea of the overall transfer function, do a quick frequency sweep to approximately locate the upper and lower corner frequencies of the amplifier gain (where the midband gain changes by 3 db). Record the approximate corner frequencies. 5. Starting at a frequency one decade below the low corner frequency (f L /10), measure the gain and the phase. Remember that a phase shift of 180 degrees and a negative sign in the gain are equivalent. 6. Repeat these measurements for the rest of the frequency range, up to about one decade past the upper corner frequency. Take enough data so that the measurements can be plotted and compared with SPICE results in the analysis section, keeping in mind that Bode plots have logarithmic axes (at high frequencies the points can be relatively spread out). Make sure you get enough points near the corner frequencies, this is where accuracy counts most. 4
Figure 3: Common source amplifier schematic. 7. Next we will measure the response of the amplifier to a square wave input. Because the amplifier gain is dependent on frequency, an input square wave will not result in a perfect square wave at the output. For a discussion of the shape of the output pulse, see Appendix D.5, pp. D12-D15. Since our circuit is a bandpass amplifier, it displays characteristics of both a high-pass and low-pass system (see Appendix D, pp. 6-9). 8. Connect a low-amplitude, high frequency square wave to the input of the amplifier (the amplitude of the input should be about 0.2 volt). Measure and record the rise time (see Fig. D-13 in the text) and fall time (which should be very close to the rise time). 9. Decrease the frequency of the square wave by several orders of magnitude and measure and record the percentage sag (see Fig. D-14 in the book). The cursor feature of the scope makes these measurements easier. 4 Analysis Answer the following questions in the analysis section of your lab report: 1. Compare your measured values for the V G, V D, and I D of M 1 to the simulated values. Do they match well, and if not, where do you think the differences come from? 5
2. Using Matlab generate Bode plots of the magnitude and phase of the transfer function, with both the simulated and measured values on the same plot. You may need to use the unwrap function in Matlab on the phase measurements, as a change in sign will be reflected by a 180 phase discontinuity. The unwrap function works on data in radians, so you may need to perform some phase conversions (see the Matlab help file for unwrap). 3. Do the simulated and measured Bode plots match well, and if not, where do you think the differences come from? In particular, is the measured upper 3dB point higher or lower than predicted by the simulation, and why? 4. Which of your upper 3dB point approximations from the pre lab (dominant pole or O.C.T.C.) matches best with the simulated and measured data? Is this what you would expect, and why? 5. In taking these measurements we used a 10x scope probe to minimize output loading on the amplifier. If instead we had used a long co-axial cable (with capacitance of 30 pf/foot) to connect the amplifier to the oscilloscope, what differences would you expect to observe in the measured transfer function, and why? 6. Using the square wave time constants from the last measurements, calculate the approximate upper and lower 3dB points for the amplifier (for an explanation of how to relate the measurements to the 3dB points, see Appendix D in the text). How do these approximations compare to the measurements? Is the single time constant assumption valid for this circuit, and why or why not? 6