Lab 2: Common Emitter Design: Part 2

Transcription

1 Lab 2: Common Emitter Design: Part 2 ELE 344 University of Rhode Island, Kingston, RI , U.S.A. 1 Linearity in High Gain Amplifiers The common emitter amplifier, shown in figure 1, will provide an equivalent linear circuit for small ac signals; however, if the gain is high then the linearity of the highest output signal levels must be measured. VCC V CC R S R 1 R C C 2 V i R 2 C 1 R E Q 1 C E R L V o Figure 1. Common Emitter Amplifier. The problem is that the operating point is set by the DC values of I C, V CE and V BE. The operating point is expected to remain constant over the entire range of ac signal voltages at the output of the amplifier. In order to understand how this works we must have a look at the total voltage between the collector and the emitter. The total voltage (ac and DC) is given by v CE (t) = V CE v ce (t) (1) where V CE is the DC voltage between the collector and the emitter, v ce (t) is the ac signal voltage between collector and the emitter, and v CE (t), is the sum of the two voltages. 1 Tel: (401) ; fax: (401) ; davis@ele.uri.edu ELE 344 Spring February 2009

2 The amplifier in figure 1 is generally a non-linear device; however, linear operation is expected if v CE V CE or V CE {v ce } peak. If this approximation does not hold then the collector current will change as the input signal changes during the ac cycle. Once this occurs then the operation will become nonlinear. 2 Quantifying Nonlinearity Linearity assumes that the relation between the output voltage and the input voltage is given by the following relation: v o (t) = A VS v s (t) (2) where v o (t) is the output voltage, v s (t) is the input from the source and A VS is the voltage gain with respect to the signal source. If the system is linear then A VS will remain constant over ALL input voltage levels. The graph, {v o (t)} peak vs. {v s } peak would be a straight line. Unfortunately, the voltage gain for the amplifier shown in figure 1 is only linear over a small range of ac input voltages. This means that A VS is a constant for only a small range of input voltages. Thus, a linear voltage gain is a reasonable approximation as long as V CE {v ce (t)} peak (e.g. the ac signal voltage is much smaller than the DC bias voltage). There are many methods which can be used for quantifying linearity. One method is to observe the input and output signals with an oscilloscope. Nonlinearity can be detected once the shape of the output signal, a sine wave for instance, becomes distorted. The drawback with this method is that it is difficult to detect a distorted waveform with an oscilloscope in the early stages of nonlinear operation. A second method is to use an analog or a digital spectrum analyzer. These are probably the most accurate and common methods used to make a direct measurement of distortion. There is a third method, one can measure the peak positive ac amplitude and the peak negative ac amplitude for the input and output signals. This allows one to measure the actual gain for the positive swing and the negative swing of an output signal. The amplifier gain at the peak positive and peak negative swings will be equal in a linear system; however, these values will differ for small signal levels in a high gain amplifier. In order to measure the linear gain of an amplifier, the output signal must be very small. For the system which you were required to design in the previous lab the gain should have been at least 100. This means that you will need to generate ac output signal levels much less than 1V peak in order to determine the effective gain. Then the input signal level will need to be increased from that point until the measured gain is no longer constant. 2

3 3 Measuring Nonlinearity The two tools you have to perform this measurement are the SPICE simulator in MultiSim and the bread-boarded circuit. Transient analysis is required for the SPICE simulator; this requires that an input sine wave is generated in SPICE, passed through the amplifier, and then measured at the output. Thus, in MultiSim, you will: 1) Measure v s (t) at the positive and negative peak voltages. 2) Measure v o (t) at the positive and negative peak voltages. 3) Compute A vs, the ratio of the output voltage to the source voltage. The same steps will be followed for your breadboard circuit. There are some practical problems. For the amplifier shown in figure 1 with a gain of 100, you will want the first peak values of v o (t) to be no greater than several hundred mv s. This means that the input signal level must be 100 less!! While this is not difficult to do in a SPICE simulator, you do want to reproduce these results on your breadboard circuit. The problem with the breadboard is the signal generators. Most of the signal generators used in our labs will not allow one to reliably produce sine waves with amplitudes of 1mV or less. This is also difficult to measure directly with an oscilloscope. You will need to create a source which divides the output voltage by a large value but maintains an equivalent resistance of 300Ω in order to comply with the requirements for R S. The source in figure 2 will produce a small Thevenin Equivalent voltage if R S1 R S2. If R S2 in figure 2 is set to R S in figure 1, and R S1 R S2, then an equivalent signal source can be realized. R S1 1 R S2 Figure 2. Modified signal source. 3

4 4 Lab Description Using the method described in the previous sections measure the linearity of your amplifier design from Lab1 using the SPICE simulator in MultiSim and the bread-boarded circuit. 1) Using the method described in the previous sections measure the linearity of your amplifier design from Lab1 using the SPICE simulator in MultiSim and the bread-boarded circuit. 2) Select R S1 values of 1MΩ, 100kΩ and 10kΩ. Find an expression for v s (t) as a function of v 1 s(t) and your effective source resistance, R S as a function of R S1 and R S2. Note that R S = 300Ω!! 3) Measure and record the values of each resistor, e.g. the 1MΩ, 100kΩ and 10kΩ resistors used for R S1 and R S2. Compute the effective R S (for each R S1 value). 4) Record the values of v s (t) and v o (t) for each sinusoidal input voltage for both positive and negative peak voltage levels. 5) Estimate the linear voltage swing of your amplifier. 6) Redesign your amplifier; this time set the DC operating point for 1.5mA and recompute the values of R 1, R 2 and R E. Set V CC = 15V and select an appropriate value for R C. 7) Verify the operating point for a range of β DC values. 8) Compute the amplifier gain and input impedance. 9) Verify the operating point using the SPICE simulator in MultiSim. 10) Add a resistor, R x, with a value of approximately 160Ω. Connect R x as shown in figure 3. 11) Find the new value of I C. 12) Find the ac equivalent small signal model for the amplifier in figure 3. 13) Compute g m & r π. 14) Find an expression for A Vin, A VS and Z in. 4

5 VCC V CC R 1 R C C 2 R S V i C 1 R 2 R E Q 1 C E R L V o R x Figure 3. Modified Common Emitter Amplifier. 15) Compute these values and verify them using the SPICE simulator in MultiSim. 16) Measure the linearity of the amplifier in figure 3 using the SPICE simulator in MultiSim and the bread-boarded circuit. 5 Write Up Include the following results in your write up: 1) Record the values of the resistors from steps 2 and 3. 2) Record the expressions for v s (t) as a function of vs 1 (t) and your effective source resistance, R S as a function of R S1 and R S2. Note that R S = 300Ω!! 3) Estimate the effective value of R S for each resistor used in the voltage divider, using R S1 and R S2. 4) Create a table with 3 columns, {v 1 s(t)} peak, {v o (t)} peak, and A VS ; remember to record the positive and negative peak values. 5) Plot {v o (t)} peak vs. {v 1 s(t)} peak using the measured values; overlay this plot with the line used from the small input voltages used to estimate the actual amplifier gain. For the second part of this lab with the amplifier in figure 3: 5

6 1) Record the steps used in your design. 2) Record the values of R 1, R 2, R E and R C. 3) Show your work for the computed I C vs. β DC. 4) Record the computed values for g m and r π. 5) Show your expressions for A Vin, A VS and Z in ; also show the computed values. 6) Create a table with 3 columns, {v 1 s(t)} peak, {v o (t)} peak, and A VS ; remember to record the positive and negative peak values. 7) Plot {v o (t)} peak vs. {v 1 s(t)} peak using the measured values; overlay this plot with the line used from the small input voltages used to estimate the actual amplifier gain. Compare the two amplifiers, your design of the amplifier in figure 1 and the amplifier designed using the schematic in figure 3. Answer the following questions: 1) Does the inclusion of the resistor, R x, improve the overall linearity? 2) What is the cost of adding R x? 3) Would you expect that A Vin, that is the voltage with respect to V in (or V i in the schematics) will also change when A VS is changing? 4) Does it seem possible to have a peak output voltage swing of 3V for either amplifier topology? 6