This version (22 Nov 2018 16:04) was *approved* by dmercer.The Previously approved version (21 Nov 2018 14:53) is available.

The objective of this activity is to investigate the frequency response of the common emitter amplifier configuration using an NPN BJT transistor.

As in all the ALM labs we use the following terminology when referring to the connections to the M1000 connector and configuring the hardware. The green shaded rectangles indicate connections to the M1000 analog I/O connector. The analog I/O channel pins are referred to as CA and CB. When configured to force voltage / measure current -V is added as in CA-V or when configured to force current / measure voltage -I is added as in CA-I. When a channel is configured in the high impedance mode to only measure voltage -H is added as CA-H.

Scope traces are similarly referred to by channel and voltage / current. Such as CA-V , CB-V for the voltage waveforms and CA-I , CB-I for the current waveforms.

The schematic of a typical common-emitter amplifier is shown in figure 1. Capacitors C_{B} and C_{C} are used to block the amplifier DC bias point from the input and output (AC coupling). Capacitor C_{E} is an AC bypass capacitor used to establish a low frequency AC ground at the emitter of Q_{1}. Miller capacitor C_{F} is a small capacitance that will be used to control the high frequency 3-dB response of the amplifier.

Figure 1: Common-emitter BJT amplifier.

For this section, assume that C_{B} = C_{C} = C_{E} = 1 Farad and C_{F} = C_{Π} = C_{µ} = 0. You can find the DC collector current (I_{C}) and the resistor values following the analysis provided in your text book. Since the topology and the requirements might be slightly different than in the text, you will need to make minor modifications to the design procedure and equations.

Figure 2 shows the low-frequency small-signal equivalent circuit of the amplifier. Note that C_{F} is ignored since it is assumed that its impedance at these frequencies is very high. R_{B} is the parallel combination of R_{B1} and R_{B2}.

Figure 2: Low-frequency equivalent circuit.

Using short-circuit time constant analysis, the lower 3-dB frequency (ω_{L}) can be found as:

Where:

Figure 3 shows the high-frequency small-signal equivalent circuit of the amplifier. At high frequencies, C_{B}, C_{C} and C_{E} can be replaced with short circuits since their impedance becomes very small compared to R_{S}, R_{L} and R_{E}.

Figure 3: High-frequency equivalent circuit.

The higher 3-dB frequency (ω_{H}) can be derived as:

Where:

Thus, if we assume that the common-emitter amplifier is properly characterized by these dominant low and high frequency poles, then the frequency response of the amplifier can be approximated by:

Assuming C_{B} = C_{C} = C_{E} = 1 Farad and C_{F} = C_{Π} = C_{µ} = 0, and using a 2N3904 transistor, design a common-emitter amplifier with the following specifications:

V_{CC} = 5 V

R_{S} = 50Ω

R_{L} = 1 kΩ

R_{IN} > 250

Isupply < 8mA

A_{V} > 50

peak-to-peak unclipped output swing > 3 V

1. Show all your calculations, design procedure, and final component values.

2. Verify your results using the LTSpice circuit simulator. Submit all necessary simulation plots showing that the specifications are satisfied. Also provide the circuit schematic with DC bias points annotated.

3. Using LTSpice, find the higher 3-dB frequency (f_{H}) while C_{F} = 0.

4. Determine Cp, Cµ and r_{b} of the transistor from the simulated operating point data, (refer to your simulator's documentation on how to obtain operating point data). Calculate f_{H} using the equation from section 1.3 and compare it with the simulation result obtained in Step 3. Remember that the equation gives you the radian frequency and you need to convert to Hz.

5. Calculate the value of C_{F} to have f_{H} = 5 kHz. Simulate the circuit to verify your result, and adjust the value of C_{F} if necessary.

6. Calculate C_{B}, C_{C}, C_{E} to have f_{L} = 500 Hz. Simulate the circuit to verify your result, and adjust the values of capacitors if necessary.

7. Be prepared to discuss your design at the beginning of the lab period with your TA.

The objective of this section of the Lab Activity is to validate your pre-Lab design values by building the actual circuit and measuring its frequency response performance.

ADALM1000 Active Learning Module

Solder-less breadboard

6 - Resistors various values from the ADALP2000 Analog Parts Kit

4 - Capacitors various values from the ADALP2000 Analog Parts Kit

1 - small signal NPN transistor (2N3904)

Note on the source resistor R_{S}: because of the relatively high gain of your design you will need an input signal with a small amplitude of around 100mV. Rather than turning down the AWG in software it would be better from a noise point of view to insert a resistor voltage divider between the AWG output and your circuit input to attenuate the signal. Using something like that shown in figure 4 will provide both an attenuation factor of 1/8 and a 60Ω equivalent source resistance. Other combinations of resistor values are of course also possible based on what you have available.

Figure 4 Signal attenuator with 60Ω source resistance

Construct the CE amplifier, based on the schematic in figure 5. Figure 5b shows an example breadboard layout for the circuit.

Figure 5, Common Emitter amplifier breadboard schematic

Figure 5b Example breadboard layout

1. Use the values you designed in the pre-lab. Based on your design values from the pre-Lab, use the closest standard value from your kit. Remember that you can combine the standard values in series or parallel to get a combined value closer to your design number.

2. Check your DC operating point by measuring I_{C}, V_{E}, V_{C} and V_{B}. If any DC bias value is significantly different than the one obtained from simulation, modify your circuit to get the desired DC bias before moving onto the next step.

3. Measure Isupply.

4. Use the Bode Plotting instrument in the ALICE desktop software to obtain the magnitude of the frequency response of the amplifier from 50 Hz to as high as 20 KHz and determine the lower and upper 3-dB frequencies f_{L} and f_{H}.

5. At mid-band frequencies, measure A_{V}, R_{IN}, and R_{OUT}.

6. Measure the maximum un-clipped output signal amplitude.

7. Prepare a data sheet showing your simulated and measured values.

8. Be prepared to discuss your experiment with your TA. Have your lab data sheet checked off by your TA before submitting the lab report.

Figure 6 Alice Bode plot with C_{2} = 0.01uF and 0.047uF

Figure 7 Oscilloscope plot with C_{2} = 0.047uF at frequency = 1.5KHz

For further experimentation replace each capacitor with ones that are factors of 2 and 10 larger and smaller than your design values and re-measure the response curve with the Bode Plotting instrument. Do this to only one capacitor at a time to observe its individual effect on the response. Explain the changes in the response that you see.

**Resources**

- LTSpice files: freq_resp_bjt_ltspice

**Return to Lab Activity Table of Contents**

university/courses/alm1k/alm-lab-ce-freq-resp.txt · Last modified: 22 Nov 2018 16:04 by dmercer