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Op-Amp Closed-Loop Bandwidth Calculator

Calculate op-amp closed-loop -3dB bandwidth from the gain-bandwidth product (GBW), determine rise time, and verify phase margin.

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Formula

BW=GBWACL,tr=0.35BWBW = \frac{GBW}{A_{CL}},\quad t_r = \frac{0.35}{BW}

Reference: Texas Instruments, "Op Amp Applications Handbook"

GBW— Gain-bandwidth product (Hz)
A_CL— Closed-loop gain (V/V)
BW— -3dB bandwidth (Hz)
t_r— 10-90% rise time (s)

How It Works

Op-amp bandwidth calculator computes closed-loop bandwidth from gain-bandwidth product (GBW) — essential for audio amplifier design, active filter synthesis, and high-speed signal conditioning. Analog designers, audio engineers, and data acquisition specialists use this to verify that amplifier bandwidth exceeds signal requirements with adequate margin. Per Horowitz & Hill 'Art of Electronics' (3rd ed., p.233), for voltage-feedback op-amps, bandwidth × gain = GBW (constant). A 10MHz GBW op-amp at gain = 100 has only 100kHz bandwidth. Rise time relates to bandwidth: t_rise = 0.35/BW (10%-90% rise time for single-pole response). For multi-stage amplifiers, total bandwidth follows BW_total = BW_single / √n for n identical stages.

Worked Example

Design a 3-stage audio preamplifier with total gain = 1000 (60dB) and bandwidth > 50kHz using TL072 (GBW = 3MHz). Option 1: Single stage gain = 1000, BW = 3MHz/1000 = 3kHz — insufficient. Option 2: Three stages of gain = 10 each, per-stage BW = 3MHz/10 = 300kHz. Total bandwidth = 300kHz/√3 = 173kHz — exceeds 50kHz requirement with 3.5× margin. Rise time per stage: t_r = 0.35/300kHz = 1.17μs. Cascaded rise time: t_r_total = √(3 × 1.17²) = 2.0μs. Slew rate check: for 10Vpeak at 20kHz, SR_min = 2π × 20kHz × 10V = 1.26V/μs. TL072 SR = 13V/μs provides 10× margin.

Practical Tips

  • ✓Design for BW > 5× signal bandwidth to maintain <1° phase error at maximum signal frequency per control system design guidelines
  • ✓For gains > 10, verify phase margin on datasheet — some op-amps require external compensation capacitor to prevent oscillation
  • ✓Use current-feedback amplifiers (AD8009, OPA695) for constant bandwidth regardless of gain — ideal for video and RF applications requiring BW > 100MHz

Common Mistakes

  • ✗Assuming GBW is valid at all gains — GBW decreases at very low gains (<2) due to phase margin degradation; verify on datasheet Bode plot
  • ✗Ignoring multi-stage bandwidth reduction — cascading three identical stages reduces total bandwidth by factor of √3 = 1.73 per cascading formula
  • ✗Confusing GBW with slew rate — GBW limits small-signal bandwidth; slew rate limits large-signal bandwidth. Both must be verified for full-swing operation

Frequently Asked Questions

GBW is the frequency where open-loop gain drops to unity (0dB), typically 1-100MHz for general-purpose op-amps. For voltage-feedback types, closed-loop bandwidth = GBW/gain. An LM358 (GBW = 1MHz) at gain = 10 has 100kHz bandwidth; an OPA2134 (GBW = 8MHz) at the same gain has 800kHz bandwidth.
Inversely proportional for voltage-feedback op-amps: BW = GBW/gain. Doubling gain halves bandwidth. At gain = 1 (unity-gain buffer), bandwidth equals GBW (or less due to phase margin constraints). At gain = 100, bandwidth is 1/100 of GBW. Current-feedback op-amps maintain constant bandwidth regardless of gain.
For single-pole response: t_rise(10%-90%) = 0.35/BW. A 100kHz bandwidth yields 3.5μs rise time. For multi-pole response (Butterworth): t_rise = 0.35/BW × √n where n = number of poles. This relationship per Elmore delay analysis is fundamental to high-speed design.
GBW > gain × required_bandwidth × margin. For gain = 50 with 100kHz bandwidth and 2× margin: GBW > 50 × 100kHz × 2 = 10MHz. Select op-amps like OPA2134 (8MHz), AD8605 (10MHz), or OPA365 (50MHz). Verify slew rate meets large-signal requirements separately.

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