- 2071 Chaitra · 4+3 marks
Slew-rate check for four input signals
Short answer
For the inverting amplifier (gain 33), V2 and V3 require slopes 0.578 V/µs and 0.66 V/µs, exceeding the 0.5 V/µs slew rate, so they distort. To avoid distortion, gain must be ≤25, so feedback resistor ≤250 kΩ.
The op amp in the given figure has slew rate of 0.5 V/μS. The input signals are as follows: V1 = .01 sin 10⁶t, V2 = .05 sin (350 × 10³)t, V3 = .1 sin (200 × 10³)t, V4 = .1 sin (50 × 10³)t. [Figure: inverting amplifier: Vin through 10 KΩ to the inverting input, feedback resistor 330 KΩ from output V0 to the inverting input, non-inverting input grounded.] Determine whether the output will get distorted due to slew rate limitation? Find the new value of feedback resistor such that none of the signals gets distorted.
Given: inverting amplifier with R1 = 10 kΩ, Rf = 330 kΩ, so |Av| = 330/10 = 33. SR = 0.5 V/µs = 0.5 × 10⁶ V/s.
For an input Vp sin ωt, the output is 33·Vp sin ωt and its maximum slope is ω × 33 × Vp. The output is undistorted only if this is ≤ SR.
Check each signal
| Signal | Vp (V) | ω (rad/s) | Output peak (V) | ω·Vm (V/µs) | Distorted? |
|---|---|---|---|---|---|
| V1 | 0.01 | 10⁶ | 0.33 | 0.330 | No |
| V2 | 0.05 | 3.5 × 10⁵ | 1.65 | 0.578 | Yes |
| V3 | 0.1 | 2 × 10⁵ | 3.3 | 0.660 | Yes |
| V4 | 0.1 | 5 × 10⁴ | 3.3 | 0.165 | No |
V1: 10⁶ × 33 × 0.01 = 0.33 × 10⁶ V/s < 0.5 → OK
V2: 3.5×10⁵ × 33 × 0.05 = 0.5775× 10⁶ V/s > 0.5 → distorted
V3: 2×10⁵ × 33 × 0.1 = 0.66 × 10⁶ V/s > 0.5 → distorted
V4: 5×10⁴ × 33 × 0.1 = 0.165 × 10⁶ V/s < 0.5 → OK
V2 and V3 will be distorted by slew-rate limiting; V1 and V4 will not.
New feedback resistor
For each signal the maximum gain allowed is Av(max) = SR/(ω·Vp):
V1: 0.5×10⁶ / (10⁶ × 0.01) = 50
V2: 0.5×10⁶ / (3.5×10⁵ × 0.05) = 28.57
V3: 0.5×10⁶ / (2×10⁵ × 0.1) = 25
V4: 0.5×10⁶ / (5×10⁴ × 0.1) = 100
The smallest limit is 25 (set by V3), so the gain must be ≤ 25:
Rf ≤ 25 × R1 = 25 × 10 kΩ = 250 kΩ
Answer: V2 and V3 are distorted; use Rf ≤ 250 kΩ (e.g. a standard 240 kΩ or 220 kΩ) so that none of the signals is distorted. (This treats each signal applied separately, which is the usual reading; if all four were applied together, the slopes could add and a still smaller gain would be needed.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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