1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics. R₂ HH Ri C₁ + Figure 1: Differentiator circuit. (a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal op-amp: Vo Gain= = V₁ -jwC₁R₂ (1+jwC₁R₁) (b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R₂ is 120 ks?, design the rest of the component values. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 10% Hz. (d) The input signal v, to this differentiator is as shown in Fig. 2. Voltage (mV) 50 50 -50 0 100 200 300 t[ms] Figure 2: Signal applied to the differentiator. (i) Will this signal be differentiated when passing through the circuit given in Fig. 1? Vi (ii) On a clearly labelled graph, sketch the input u, and the output of the circuit in Fig. 1. Cal- culate the significant voltage values and mark all main features in your graph.
1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics. R₂ HH Ri C₁ + Figure 1: Differentiator circuit. (a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal op-amp: Vo Gain= = V₁ -jwC₁R₂ (1+jwC₁R₁) (b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R₂ is 120 ks?, design the rest of the component values. (c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 10% Hz. (d) The input signal v, to this differentiator is as shown in Fig. 2. Voltage (mV) 50 50 -50 0 100 200 300 t[ms] Figure 2: Signal applied to the differentiator. (i) Will this signal be differentiated when passing through the circuit given in Fig. 1? Vi (ii) On a clearly labelled graph, sketch the input u, and the output of the circuit in Fig. 1. Cal- culate the significant voltage values and mark all main features in your graph.
Introductory Circuit Analysis (13th Edition)
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Please answer all parts of the question with step by step working and explanantions so i understand the questions and solution better thank you. Please include neat sketch of bode plot and how you obtained the values.
![1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics.
R₂
HH
Ri
C₁
+
Figure 1: Differentiator circuit.
(a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal
op-amp:
Vo
Gain=
=
V₁
-jwC₁R₂
(1+jwC₁R₁)
(b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R₂ is 120 ks?,
design the rest of the component values.
(c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 10% Hz.
(d) The input signal v, to this differentiator is as shown in Fig. 2.
Voltage (mV)
50
50
-50
0
100
200
300
t[ms]
Figure 2: Signal applied to the differentiator.
(i) Will this signal be differentiated when passing through the circuit given in Fig. 1?
Vi
(ii) On a clearly labelled graph, sketch the input u, and the output of the circuit in Fig. 1. Cal-
culate the significant voltage values and mark all main features in your graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7912362-195e-4ab5-9ace-9dd5581a1ab8%2F7909d518-7a15-46dc-80b8-5058e614ce58%2Fvqx5d7_processed.png&w=3840&q=75)
Transcribed Image Text:1. The differentiator circuit shown in Fig. 1 uses an op-amp with ideal characteristics.
R₂
HH
Ri
C₁
+
Figure 1: Differentiator circuit.
(a) Prove that the gain of the circuit is given by the following expression using first principles for an ideal
op-amp:
Vo
Gain=
=
V₁
-jwC₁R₂
(1+jwC₁R₁)
(b) The differentiator has unity gain at 1 kHz and the high frequency gain is 40 dB. If R₂ is 120 ks?,
design the rest of the component values.
(c) Sketch the Bode magnitude response for this circuit for the frequency range of 10° to 10% Hz.
(d) The input signal v, to this differentiator is as shown in Fig. 2.
Voltage (mV)
50
50
-50
0
100
200
300
t[ms]
Figure 2: Signal applied to the differentiator.
(i) Will this signal be differentiated when passing through the circuit given in Fig. 1?
Vi
(ii) On a clearly labelled graph, sketch the input u, and the output of the circuit in Fig. 1. Cal-
culate the significant voltage values and mark all main features in your graph.
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