Lab_3_Report_Christian-323

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11/1/2023 CHRISTIAN M ANDRADE SAURABH SACHDEVA Differential Amplifier

Objective The purpose of this experiment is to design and test differential amplifiers. In the experiment, we are given a set of specifications and our task is to choose resistor values for the differential amplifier design to meet these specifications. Then, after creating the design we will simulate it, then build and test to make sure the practical circuit fits our specification. PreLab First, we started by performing the required calculations to meet the specifications of our design Calculations. We first calculated the value of RS and RC1,2 using the assumptions, Rs >> RE B=100, RE = 0, we got: Ic1 = Ic2 = Ic = 100•Ib = 100•20uA = 2mA lee = 2•lc = 4mA Ve Vcq= 3V Vcc - Ic•RC=Vcq RC = (Vcc - Vcq)/Ic = 1.5kohms Vee = Ve - RS•lee RS = (Ve - Vee)/lee = (-0.7 -(-6)) V / 4mA= 1.325kohms So, RC1= RC2=1.5kohms, and RS= 1.325kohms. Rounding to the nearest standard resistor values, we got RCI= RC2= 1.5kohms, and RS= 1.3kohms.

Using the resistor values we found for the design, we calculate the value required by the specifications table. The calculations are shown below.

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Simulations After performing the calculations, we moved on to performing the required simulations. We first set up the circuit as shown in Figure below to perform a DC sweep to get the voltage transfer characteristic and use it to estimate the small signal gain. We used a non-ideal transistor to include the parasitic components.

We performed a DC sweep between -0.1 V to 0.1 V, and we got the following results shown in Figure below. As seen from the Figure the single-sided small signal gain is found from the slope around. Vin-0, we find that it's 56.5 V/V, which translates to a differential gain of 2*56.5= 113 V/V. We then built the circuit shown in Figure 3 below to perform a frequency response analysis of the differential pair. As seen from the figure, we have a mid-band gain of 54.5 V/V (109 V/V differential gain) and a 3dB frequency of 27.1 MHz. Post lab The Gain over Frequency We built the designed differential amplifier on the breadboard and connected it to the function generator and adjusted it to generate a voltage that produce and output of 1 Vpp, then we varied the frequency and measure the gain to determine the frequency response. The resulting frequency response is shown in Figure below.

As seen from the Figure the experimental bandwidth of the physical differential amplifier is very narrow compared to the simulated one, this can be attributed to capacitances of the wires and breadboard rails which can produce many undesired poles. The differential gain is 108 V/V which matches closely with the calculated and simulated gains. The 3dB frequency is 4.1Mhz which differs widely from the simulated value of 27 MHz, this could be also attributed to the same poles introduce by unwanted capacitances in the circuit that narrowed the bandwidth. Phase Then, we measured the phase difference between the collectors of the two transistors in the differential pair. The result is shown in the Figure below. As seen from the figure, the phase difference between the two transistors is 179.40, which is very close to the expected value of 180° Common Mode Gain Then, we connected the two inputs of the differential amplifier together and tested it with a signal with 10 KHz to measure the common mode gain. The resulting input and output waveforms are shown in Figure below.

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As seen from the figure, the common mode gain is 1.36 V/2.24V= 0.6 V/V. This value matches closely with our calculated common mode gain of 0.58 V/V. Input Offset Voltage We grounded both inputs of the amplifier and measured the voltage difference between the two collectors, we found that voltage difference is -57.8 mV, which translates to an input offset -57.8 mV/108=-0.54 mV. Conclusion Therefore, we learned how to design and test differential amplifiers. We also learned about the non- ideal characteristics of such devices that affect their gain and frequency response. In the future, we should use our amplifiers to extend their bandwidth.