Operational Amplifier - Assignment | Solid State Physics, Devices & Electronics PDF Download

Q.1. (a) An op-amp has CMRR = 100dB , differential gain A_D = 5 and common mode voltage applied to it is 3 mV . Find the value of common mode output voltage.
(b) An op-amp has differential gain A_D = 100 . Common mode voltage applied to it is 3 mV and corresponding output voltage is 0.03 μV . Find the value of CMRR in dB.

(a) CMRR(in dB) = 20log₁₀(A_D/A_CM)

∵ A_CM = V_oCM/V_CM = 5 x 10^-5 ⇒V_oCM = 5 x 10^-5 x 3 x 10^-3V = 15 x 10^-8V = 0.15μV

Q.2. Consider the circuit shown in figure below.

(a) Find the frequency above which the gain will decrease by 20 dB per decade.
(b) Find the magnitude of gain at operating frequency of 40 kHz.
(c) Find the phase angle (∅) at 40 kHz.

Q.3. For the circuit shown in figure draw output waveform.
(a) 

(b)

v_id = v₁ - v₂ = v_in - 2.5V ∵
∵ v_in < 2.5V ⇒ v_id = -ve
∵ v_in > 2.5V ⇒ v_id = +ve
(b) 

Q.4. Consider the circuit shown in figure below.

(a) Find the frequency above which the gain will decrease by 40 dB per decade.
(b) Find the magnitude of gain at operating frequency of 20 kHz.

Q.5. An amplifier has a voltage gain of 500, input impedance 20 kΩ, output impedance 75 Ω and bandwidth is 10 Hz without any feedback. Now a negative feedback with β = 0.1 is applied. Find
(a) Its gain
(b) Input impedance
(c) Output impedance
(d) Its bandwidth

(b) R_iF = R_i (1 + AB) = 20k x (1 + 500 x 0.1) = 1020kΩ
(c) R_oF = R₀/(1+AB) = 75/(1 + 500 x 0.1) = 1.5Ω
(d) f_oF = f₀(1+AB) = 10(1 + 500 x 0.1) = 510Hz

Q.6. Consider the circuit shown in figure below.

(a) Find the frequency upto which the gain will increase by 20 dB per decade.
(b) Find the magnitude of gain at operating frequency 4 kHz and 6 kHz.
(c) Find the phase angle (∅) at 6 kHz.

At 4kHz,
At 6kHz,
(c)

Q.7. Find the output voltage V₀ of the OPAMP circuit shown in figure below

(b)

⇒ V0 = 8V

(b)


⇒ V₀ = K₁V₁ + K₂V₂

Q.8. Consider the circuit shown in figure below.

(a) Find the frequency upto which the gain will increase by 40 dB per decade.
(b) Find the magnitude of gain at operating frequency of 2 kHz.

Q.9. In an ideal Op-Amp circuit shown below V_i = V_m sinωt.
(a) Find the amplitude of V₀.
(b) Find the peak value of current through R₁.
(c) Find the peak value of current through R₂ .
(c) Find the peak value of potential at P. 

(b) Current through R₁ is
Peak value of current = Vm/R₂
(c) Current through R2 is
Peak value of current = V_m/R₂
(d) Peak value of voltage at P is = V_m.

Q.10. The input to a lock-in amplifier has the form V_i(t) = V_i sin(ωt+60) where V_i, ω and 60⁰ are the amplitude, frequency and phase of the input signal respectively. This signal is multiplied by a reference signal of the same frequency ω, amplitude V_r and phase 30⁰.
(a) If the multiplied signal is fed to a high pass filter of cut-off frequency ω, find the final output signal.

(a) If the multiplied signal is fed to a low pass filter of cut-off frequency ω, find the final output signal.

(b) If the multiplied signal is fed to a High pass filter of cut-off frequency ω, find the final output signal.

V = V_rsin(ωt+30) x V_isin(ωt+60) = V_iV_r/2[cos(60-30) -cos(2ωt+60+30)]

(a) Output of Low pass filter
(b) Output of high pass filter

Q.11. For the circuit shown in figure the output is V_o = -2V₁ +3V₂ - V₃. Find the values of resistances R₁, R₂ and R₃.

⇒ V_o = -2V₁ + 3V₂ - V₃
Thus R₁ = 3kΩ, R₂ = 2kΩ and R₃ = 6kΩ.

Q.12. Consider a Low Pass (LP) and a High Pass (HP) filter with cut-off frequencies f_LP and f_HP, respectively, connected in series or in parallel configurations as shown in the Figures A and B below. 

Find the response of Filter A and B if
(a) f_HP < F_LP (b) f_HP > f_LP

(a) f_HP < F_{LP
A acts as a Band Pass filter, B allows the signal from passing through
(b) fHP > fLP}
A stops the signal from passing through, B acts as a Band Reject filter

Q.13. For the circuit shown in figure R₁ = R₂ = R₃ = 2Ω, L = 1μH and C = 1μF . If the input is v_in = cos(10⁶t), then |v₀/v_in| is

Output of first Op-Amp is

Output of second Op-Amp is

Q.14. Consider the Op-Amp circuit shown in figure.

If V_i = V₁sin(ωt) and V₀ = V₂ sin(ωt + ∅), then find
(a) magnitude of the gain
(b) the phase angle (∅) at ω → 0 and w → ∞.

Thus ∅ = -2tan^-1(ωRC).
(a) Magnitude of the gain is 1.
(b) The phase angle (∅) at w → 0 is ∅ = 0 and at ω → ∞ is ∅ = -π.

Q.15. In the op-amp circuit shown in the figure, V_i is a sinusoidal input signal of frequency 10 Hz and V_o is the output signal.
(a) Find the magnitude of the gain.
(b) Find the phase of the output signal.

 
(b) Phase of the output signal ∅ = π - θ = π - tan^-1 (ωCR_F)
θ = tan^-1 (2 x 3.14 x 10 x 10^-8 x 10⁴) = tan^-1 (6.28 x 10^-3) ≈ 0
⇒ ∅ = π - θ ≈ π

Q.16. The circuit in figure employs positive feedback and is intended to generate sinusoidal oscillation. If at a frequency  then to sustain oscillation at this frequency find R₂.

Apply KCL at node 1

Q.17. Figure shows a practical integrator with R_S = 30MΩ, R_F = 20MΩ and C_F = 0.1μF. If a step (dc) voltage of +3V is applied as input for 0 ≤ t ≤ 4 (t is in seconds), then draw output voltage as a function of input voltage.

⇒ V₀ = -t Volts
A ramp function of peak voltage -4V.

Q.18. For the circuit in shown in figure below find output frequency frequency f₀ and resistance R_F. 

The circuit shown in figure is Phase Shift Oscillator.
The frequency of oscillation f₀ and is given by
 
At this frequency, the gain A_u must be at least 29. That is,
⇒ R_F = 957kΩ

Q.19. In the Op-Amp circuit shown, assume that the diode current follows the equation I = I₀exp(V/V_T). For V_i = 2V, V₀ = V₀₁ and for V_i = 8V, V_o = V₀₂. At room temperature of 27⁰ C find the value of (V₀₁-V₀₂).

At room temperature of 27⁰C, V_T = 26mV
⇒ V₀₁ - V₀₂ = 2V_T ln 2 = 2 x 26 x 0.693mV ≈ 36mV

Q.20. For the circuit in shown in figure below if output frequency frequency f₀ = 965Hz find R and R_F. 

The circuit shown in figure is Wein Bridge Oscillator.

At this frequency R_F = 2R₁ = 2 x 12 = 24kΩ

Q.21. Consider the following circuit
Draw output V_out corresponding to the input V_in.

 

It’s a inverting comparator with positive feedback. Output is forced to operate in saturation region.

Q.22. The OP-AMP circuit shown in figure is a bistable multivibrator. Let the OP-AMP saturation voltages be ±10V, C = 0.01 µF, R₁ = 200kΩ, R₂ = 2MΩ and R = 2MΩ.

(a) Calculate the positive and negative threshold voltage at the inverting terminal for which the multi-vibrator will switch to other state.
(b) Calculate the frequency of the oscillation. Sketch the voltage (V_OUT) waveform.

(a) Threshold voltage
(b) The time period T of the output waveforms is given by