Differential Amplifier

1. Objective:

Simulate and implement a BJT differential amplifier with a current source.

2. Theory:

A differential amplifier is that kind of an amplifier that amplifies the difference between two voltages and rejects the average or common mode value of the two voltages. If v1 and v2 are the two DC voltage .Differential mode V_idm and Common mode V_icm input voltage are given by

V_idm = v1 + v2 ---I

V_icm = (v1+v2)/2---II

And the output voltage Vout is given by

V_out = V_icm ∗ A_cm + V_idm ∗ A_dm ---III

Where A_cm and A_dm are common mode and differential mode gain. Which can be expressed as

And the Common Mode Rejection Ratio (CMMR) is given by

CMMR = 20log| A_dm⁄A_cm |---- VI

Also

gm=I_c/nV _t---VII

3. Equipment Used

• Breadboard
• 2N2222 NPN Transistor
• DC power supply
• Wires
• Resistors
• LT Spice IV

4. Schematics and simulation:

5. Results and Discussions

For this experiment we used superposition to find out V_out. Since, equipment provided at the lab was unable to measure out the V_out with DC input and AC input simultaneously. Therefore, DC analysis and AC analysis were done separately and then added together following superposition. To calculate DC experimental values on the lab, both bases of Q₁ and Q₂ were grounded. The DC biasing value simulation and experiment is shown in the Table 1.

Table 1: Simulated and measured DC values

	Simulation	Hand Calculation	Lab Result
Vout	2.786 V	2.84 V	2.88 V
Ic1	1.106 mA	1.108 mA	1.06 mA
I c2	1.106 mA	1.108 mA	1.05 mA
I c3	2.224 mA	2.16 mA	2.13 mA
I c4	2.146 mA	2.2016 mA	2.12 mA

Table 2: Resistors values

	Theoretical Value	Simulated Value	Experimental Value
Rc1	2 K	2 K	1.979 K
Rc2	2 K	2 K	1.99 K
Rbias	4.65K	4.3 K	4.27 K

Table 2 shows the resistor used to complete the circuit in the simulation and for the lab.

Then to calculate differential mode gain, Q₁ was given AC input of 115 mV. Then the output was taken from the collector of Q₁ and Q₂. At 100 Hz frequency 5.8 and 6 volts came out to be the output for the non-inverting and inverting output respectively as shown in the figure 7 and 8 respectively.

And for the common mode gain the values that I was getting was not right value because of the internal noise generated by the oscilloscope added with the circuit noise. Thus, I was getting error finding value for the common mode gain.

6. Hand Calculations

Table 4: Value obtained from hand calculation

	Experimental Value	Calculated	Simulated Value
gm	0.424	0.0432	0.04424
Acm-se	0.430	0.01	0.01
Adm-se	-42.4	-43.2	-44.24
CMMR	72.5 dB	72.7 dB	72.91 dB

The values obtained for the differential and common mode gain are shown in the table 4 with the input voltage of 115 mV. We can see in the table 3 and 4 that the common mode noise in the experiment was high where differential mode came around to be in the range of 42 to 44. Also, The CMMR was found to be 72.5 decibels on the lab with a small marginal error due to the face that common mode was higher than expected.

Again, the circuit was also tested on frequency response. Frequency was changes once output signal was seen on Oscilloscope. The frequency was varied form 100 Hz to 10MHZ. The output signal value was recorded in table 5 with the change in frequency of input. The input signal was kept constant i.e. 115 mV for the all the measurement. We can observe the pattern that output voltage decreased with the increment of the frequency.

The bode plot was plotted to find the cut off frequency for the circuit shown in figure 3. The table 5 was constructed with the output voltage with the change of frequency of a input signal shown in the figure 9. After comparing with the simulated bode plot in figure 10 with an experimental bode plot we can tell that figure 9 bode plot was not very accurate due to the noise and scope offset generated by Oscilloscope.

7. Conclusion:

This laboratory was very tedious because we had to find various aspect of the circuit. From the biasing point to AC analysis was done for the differential amplifier. Both common mode and differential mode gain were calculated as well the cutoff frequently of the amplifier was measured. Overall lab was successfully done with an error margin created by the noise and the offset of the oscilloscope.