### Objective:

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

### Common Emitter Amplifier Topology

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 Q1. Miller capacitor C_{F} is a small capacitance that will be used to control the high frequency 3 dB response of the amplifier.

### Low Frequency Response

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}.

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

Where

### High Frequency Response

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}.

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:

Where:

s is the complex angular frequency

A_{V} is the midband gain

ω_{L} is the low corner angular frequency

ω_{H} is the high corner angular frequency

#### Pre-Lab Setup

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} = 50 Ω

R_{L} = 1 kΩ

R_{IN} >250 Ω

I_{SUPPLY} <8 mA

A_{V} >50

Peak-to-peak unclipped output swing >3 V

- Show all your calculations, design procedure, and final component values.
- 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. - Using LTspice, find the higher 3 dB frequency (f
_{H}) while C_{F}= 0. - Determine C
_{π}, C_{μ}, and r_{b}of the transistor from the simulated operating point data. Calculate f_{H}using the equation from the High Frequency Response section 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. - 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. - 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.

### Lab Procedure

#### Objective:

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.

#### Materials:

- ADALM2000 active learning module
- Solderless breadboard
- Six resistors, various values, from the ADALP2000 analog parts kit
- Four capacitors, various values, from the ADALP2000 analog parts kit
- One small signal NPN transistor (2N3904)

Note that on the source resistor, R_{S}, and the AWG output of the ADALM2000, the AWG output has a 50 Ω series output resistance and you will need to include it, along with the external resistance, in series with its output. Also, due to the relatively high gain of your design, you will need an input signal with a small amplitude of around 100 mV peak-to-peak. 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 the setup shown in Figure 4 will provide both an attenuation factor of 1/16 and a 60 Ω equivalent source resistance. Other combinations of resistor values are also possible based on what you have available—in our case, a standard resistor value will be used—68 Ω.

#### Hardware Setup

Construct the circuit on your breadboard.

#### Directions

- Construct the amplifier, based on the schematic in Figure 1, 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.
- 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. - Measure I
_{SUPPLY}. - Use the network analyzer instrument in the Scopy software to obtain the magnitude of the frequency response of the amplifier from 50 Hz to 20 kHz and determine the lower and upper 3 dB frequencies f
_{L}and f_{H}. - At midband frequencies, measure A
_{V}, R_{IN}, and R_{OUT}.

Plot examples are provided using the LTspice simulations of the circuit in Figure 5.

### Question:

- Replace capacitor C
_{F}with a smaller value (0.01 μF) and remeasure the response curve with the network analyzer instrument or ac sweep simulation. Explain the effect of the new capacitor value in the response that you see.

You can find the answer at the StudentZone blog.