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Student’s Name Professor’s Name Course Date LAB REPORT ON THE DESIGN OF A DIFFERENTIAL AMPLIFIER Introduction A differential amplifier is an electronic circuit that is designed using either transistors or operational amplifiers. They give an amplified output, which is the difference between the two input signals. It has two terminals, an inverting terminal, and the non-inverting terminal (Carter and Mancini, p.3-6). During design, the principle of superposition is used to obtain resistances suitable for determining the gain. The voltage divider rule is also applied at the inverting terminal to find the voltage at the terminal. Non-inverting output equations are applied at the non-inverting terminal to find the voltage (Rashid, p.86). The gain of the circuit is a ratio of resistors R3 and R1, as shown. A dc supply of either + 5V or -5V is fed at the emitter and collector terminals to properly bias the operational amplifier. Biasing is essential in allowing the amplifier to operate in the active region by ensuring that the emitter-base junction is forward biased while the collector junction is reverse biased. The main aim of biasing is to determine the power on the differential amplifier and determine its operating points in the linear region (Rashid, p.313). Differential amplifiers are widely used because they have a larger common- mode rejection ratio, minimizing and improving the signal to noise ratio (Bakshi and Godse, p2- 6; Huijsing, p.365; Amina et al., p.236). It is also easy to bias since it involves a direct coupling among stages. For example, the biasing resistor has no effect on the circuit's gain, and no by-pass capacitors are required.
DESIGN 1
First Differential Amplifier with Input Voltage in the range of V (^) 1 = 0 v ¿ 1.5 v V (^) 2 = 0 v ¿ 1.3 v The output range V (^) out = 0 v ¿ 10 v The design calculations are performed as shown; I 1 = V (^) 1 − V (^) a R 1
; I 2 =
V (^) 2 − V (^) b R 2 ; I (^) f = V (^) a − V (^) out R 3 At the summing point V (^) a = V (^) b And V (^) b = V (^) 2
R 4
R 2 + R 4 )
When the value of V^ 2 =^0 V (^) out ( b )= V (^) 2
R 4
R 2 + R 4 )(^
R 1 + R 3
R 1 )
vout =− vout ( a )+ vout ( b ) Therefore; vout =− v 1
R 3
R 1 )
+ V 2
R 4
R 2 + R 4 )(^
R 1 + R 3
R 1 )
Assuming that the values of R 1 = R 2 and the values of R 3 = R 4
V (^) 1 = 0 v ¿ 9.5 v V (^) 2 = 0 v ¿ 9.3 v The output range V (^) out = 1 v ¿ 1.5 v The design calculations are performed as shown; I 1 = V (^) 1 − V (^) a R 1
; I 2 =
V (^) 2 − V (^) b R 2 ; I (^) f = V (^) a − V (^) out R 3 At the summing point V (^) a = V (^) b And V (^) b = V (^) 2
R 4
R 2 + R 4 )
When the value of V^ 2 =^0 V (^) out ( b )= V (^) 2
R 4
R 2 + R 4 )(^
R 1 + R 3
R 1 )
vout =− vout ( a )+ vout ( b ) Therefore; vout =− v 1
R 3
R 1 )
+ V 2
R 4
R 2 + R 4 )(^
R 1 + R 3
R 1 )
Assuming that the values of R 1 = R 2 and the values of R 3 = R 4
Then, the output voltage is expressed as V (^) out =
R 3
R 1
( V 2 − V 1 )
V (^) out =1.5 V V (^) 2 − V (^) 1 =0.2 V R 3 R 1
R 3 =7.5 ohms ∧ R 1 = 1 ohm The circuit and various components were drawn as shown
Simulation of the second differential amplifier Figure 2: Circuit simulation results The practical components used during manufacture are tabulated as shown Table 1: Components and cost Components Cost ($) 4 Resistors each 1 ohm 1.35 per piece Function Generator XFG1 168 Oscilloscope XSC1 180 AD600AQ 40 2 Resistors each 7.5 ohms 1.35 per piece 2 Resistors each 50 ohms 1.35 per piece Power supply module 100
Discussion and Analysis The differential amplifiers consisted of two terminals; an inverting terminal and a non- inverting terminal. The output voltage is directly proportional to the amplified voltage difference between the two input signals. The principle of superposition was used to determine the resistances required for the design of both amplifiers. In the first design, two resistors were used, each of 1 ohm and two resistors of 50 ohms. In the second design, two resistors each of 1 ohm and another two resistors each of 7.5 ohms. The circuit simulations are shown in figure 1, and figure 2 gives the amplified voltage difference at the amplifiers' input terminals. The voltage divider rule was used to determine the voltage at points a and b in the design calculations. At the output of the non-inverting terminal, the voltage was determined using the non-inverting output equation. The resultant output voltage is multiplied by the amplifier's stage gain, a ratio of two resistors (R3 and R1). The circuits' design rejected the common-mode sections of the input signals and, therefore, commonly used in DC stripping applications. In the simulations (Figures 1 and 2), the circuits' output is connected to channel B of the oscilloscope while the input signals are fed to channel A. The function generator in design1 supplies a peak to peak voltage of 0.75V at a frequency of 50Hz with a 50% duty cycle. In the second design, the oscilloscope's connections are maintained; however, the function generator is fed with a 4.5 peak to peak voltage at a frequency of 50Hz with a 50% duty cycle. The results were obtained from both oscilloscope and grapher in Multisim in the View Tab.
Works Cited Amina, Madiha, et al. "Analysis of common-mode rejection ratio of a CMOS differential amplifier considering all the non-idealities." 2015 2nd International Conference on Electrical Information and Communication Technologies (EICT). IEEE, 2015 Bakshi, Uday, and Godse Atul. Linear Integrated Circuits. Technical Publications, 2010. Carter, Bruce, and Ron Mancini. Op Amps for everyone. Newnes, 2017. Huijsing, Johan. Operational amplifiers. Springer Netherlands, 2011. Rashid, Muhammad H. Microelectronic circuits: analysis and design. Cengage learning, 2016.
