8.24.21 -- This lab leads students in building a simple one-stage common emmiter amplifier. Students will measure the voltages and gain of the amplifier in the LTSpice simulation and in the breadboard.
photo from https://www.free-electronic-circuits.com/circuits/60w-guitar-amplifier.html
Note that we will not be building this circuit in lab. Not yet as far as I know.
Sections 2.1-2.3 were completed as the prelab before building the CE amplifier in section 2.4.
2.1 Gain and Bandwidth
Amplifiers can either increase or decrease the amplitude of the input signal and are characterized by its gain and bandwidth. Gain is defined as Av(f) = Vo(f)/Vi(f), where f is the frequency and V is the voltage. The gain is converted to decibels (dB) with the formula Av(dB) = 20log(Av(f)). Bandwidth is defined by the range where the gain is relatively constant and is defined by the formula BW = fH - fL. Typically this is where the gain drops by about 3 dB at the Bode plot corners.
2.2 Common Emitter Amplifier
2.2a The BJT
BJT stands for "bipolar junction transistor," and there are npn and pnp transistors. The circuit symbol for a BJT is shown in Figure 2.1. For this lab, we'll only use the npn transistor for the amplifier. The collector current Ic and voltage across the collector and the emitter Vce are used draw the family of curves and determine the Q-point of the amplifier circuit.
Figure 2.1 Circuit symbols for BJT transistors
from the lab manual
Figure 2.2 BJT symbol with voltage and
current parameters from the lab manual
Figure 2.3 Example of family of
curves graph from lab manual
2.2b The DC biasing circuit
The DC biasing circuit is used to establish the Q-point (quiescent point), which is the steady-state voltage and current of the transistor with no input signal. The formulas in Figure 2.4 lay out the how to find the Q-point.
Exercise 2.1: Suppose VCC= 9.00 V, R1= 6.80kΩ, R2= 30.0 kΩ, RC= 3.00 kΩ, and Re= 470Ω. The transistor is assumed to have β = 100, and the on-voltage VBE= 0.700 V. Calculate the Q-point.
Q(2.68786 V, 1.817 mA)
Exercise 2.2: For the circuit values of the previous example suppose β varies from 70 to 300. Calculate the range over which IC and VCE vary.
Q(2.6842 V to 2.69355 V, 1.732 mA to 1.965 mA)
Figure 2.4 Formulas from lab
manual to find Q-point
2.2c Adding the AC components
A complete common emitter amplifier includes coupling capacitors (C1 and C2), one connected to the base terminal and the other connected to the collector terminal of the transistor. There is also a load resistance RL to measure the output voltage signal and a bypass capacitor Ce to short out Re. Although the presence of the emitter resistor Re doesn't seem useful, it is use to stabilize the Q-point from variations in the transistor's β value.
Figure 2.5 Complete common emitter amplifier from lab manual
Exercise 2.3: Calculate the impedance magnitude at 1kHz for C = 1pF and 1F.
C = 1pF --> Z = -j1.59155e8 Ω , C = 1F --> Z = -j159.155 Ω
Exercise 2.4: Assuming β = 100 and RL= 10k, calculate the values for gm, rπ, and the mid-band gain for the circuit of Exercise 2.1. For the gain, be sure to denote the units (typically V/V or dB).
gm = 0.072664 ℧, rπ = 1.3762 kΩ, Av = -3.14877e-6 V/V, Av(dB) = -90.0372 dB
2.3 LTspice Simulation of the CE Amp
Before assembling it in lab, the student will simulate the CE amplifier in LTSpice. The following 4-resistor biasing circuit was constructed first. The terminal voltages and the power dissipated by the circuit are found in the below bullets.
Vb = 1.87535 V, Vc = 5.35731 V, Ve = 1.16638 V
Pdiss = Vcc * I(Vcc) = 9 * (-0.00834413) = -0.075097 W
Figure 2.6 simple DC biasing circuit
Note to myself and other readers, always label the nodes in the simulated circuit. The only way I knew what each voltage represented was because I wrote them down.
Now the AC component will be aded to DC biasing circuit. A transient analysis is recorded from 0ms to 4ms. The output signal appear to stabilize after one wavelength. The simulation is found below in Figure 2.7. Based on the simulation we can calculate the gain, which is found in the below bullet.
Av = Vout/Vin = (1.126 V)/(20mV) = 56.3 V/V
Figure 2.7 CE amplifier with AC component
A Bode plot will help visualize the bandwidth of the amplifier, which is calculated below using data from the graph.
BW = fH - fL = 10MHz - 100kHz = ~9.9e6 = ~9.9MHz
Figure 2.8 Bode plot for the CE amplifier
Some addition exercises (problem 9 in the lab manual.)
a. Remove Ce, the ‘bypass capacitor’, from the circuit of Figure 2.11 and re-simulate. What happens?
When the bypass capacitor is removed the transient simulation shows that the amplitude of Vout increases greatly.
Figure 2.9 Simulation result of part a -removed Ce
b. Return to the default circuit of Figure 2.8. Swap Rb1 and Rb2 and re-simulate (you may also want to look at the DCoperating point). What happens?
When the positions of Rb1 and Rb2 are swapped, the Vout wave becomes unbalanced. The amplitude of Vout varies and it is not a clean sine wave.
Figure 2.9 Simulation result of part - swapped Rb1 and Rb2
c. Return to the default circuit. Change the input and output coupling capacitors (C1 andC2) to 1nF (“one nanofarad”). What happens?
Vout becomes a very flat wave/signal when the coupling capacitor is removed.
d. Return to the default circuit. Remove the transistor. Now re-insert it, using “CTRL-R” to rotate the part and “CTRL-E” to get a mirror image. In this way, flip the transistor (the collector and emitter) in Figure 2.8. Then, “pick new transistor” as 2N3904. What happens when you run the simulation?
It seems like the gain was greatly reduced. Vin has the smaller amplitude and Vout has the larger amplitude like earlier, but it have an amplitude of about 250 mV instead of the 1.126 V amplitude.
Figure 2.11 Simulation result of part d - swapped Rb1 and Rb2
2.4 Build and Test a Common Emitter Amplifier
Now the student will build the various amplifiers on the breadboard. The DC biasing circuit in Figure 2.6 is built first and the following voltages in the below bullets were verified. My measurement were relatively close to the simulation results.
Vb = 1.83 V
Vc = 5.5 V
Ve = 1.11 V
Vbe = 0.72 V
Vce = 4.38 V
Changes in the load resistance are used to observe the changes in voltage gain. Table 2.1 shows the data for Figure 2.12
RL(Ω) | actual RL(Ω) | voltage gain (V/V) |
10 | 10.3 | 2.06897 |
100 | 97.2 | 12.9032 |
1k | 0.981k | 48.2759 |
10k | 9.75k | 66.3793 |
100k | 98.6k | 64.0625 |
Table 2.1 Gain compared to Load resistance
Figure 2.12 Plot of Gain with changes in load resistance
Next, the changes in frequency are used to observe the effect on the gain. Table 2.2 displays the data for the plot in Figure 2.13.
frequency (Hz) | Vin | Vout | Gain(dB) |
100 | 25.2m | 248m | 19.861 |
300 | 24.6m | 544m | 26.8933 |
1k | 24.4m | 1.10 | 33.0801 |
3k | 24.2m | 1.40 | 35.2463 |
10k | 24.4m | 1.44 | 35.4195 |
30k | 25.6m | 1.48 | 35.2404 |
100k | 24.8m | 1.48 | 35.5162 |
300k | 24.8m | 1.36 | 34.7817 |
1M | 25.6m | 840m | 30.3208 |
3M | 24.8m | 440m | 24.98 |
10M | 24.8m | 148m | 15.5162 |
Table 2.2 Bode Plot Data for CE amp
Figure 2.13 Bode Plot for gain observing changing input frequency
Conclusion
Amplifiers can be fairly easy circuits to build with not much complicated math as some circuits. In the two cases of varying the load resistance and varying the input frequency, the circuit produced data that graphed a hump that rose, then stabilized at a certain gain, and then decreased as the frequency or load resistance increased. The gain can also vary by changing the values of the coupling capacitors, changing the orientation of the transistor, or swapping the basee resistors in the 4-resistor amplifier system. It also appears that not having the bypass capacitor will stabilize the amplified output signal, even though its purpose is to reduce interference and noise.
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