ProcirelAmplifier Frequency Response: Bandwidth, Poles and Flatness
Gain is only meaningful with frequency attached. An amplifier “with gain 100” might deliver it from DC to 10 kHz or 20 Hz to 200 kHz utterly different tools. Frequency response is where coupling capacitors, feedback and GBW limits expose their intentions.
> At a glance: 7 minute guide · part 8 of 10 in the amplifiers complete guide track · includes a worked example and a quick-reference table.
## Poles, rolls and dB per decade
Every RC in the signal path contributes a pole. Response falls at −20 dB/decade beyond its corner. Coupling capacitors roll the bottom (high-pass at f = 1/2πRC), stray and load capacitance roll the top. Cascades stack: two poles begin −40 dB/decade.
| Element | Contribution | Corner formula |
| — | — | — |
| Coupling C + R | High-pass (bass roll) | 1 ÷ 2πRC |
| Miller C | High-frequency pole | Gb-limited |
| Feedback | Extends flat band | GBW ÷ gain |
| Slew rate | Large-signal ceiling | 2πf·Vpk |
| Load capacitance | Peak or roll | Isolation resistor |
## Feedback flattens what it can
What this means at the bench: Negative feedback trades gain for bandwidth the constant gain-bandwidth product. It also linearises response inside the loop. Outside the loop, op-amp output current and slew rate clip transients long before sine-wave bandwidth suggests.
## Specifying bandwidth honestly
Quote the −3 dB points and the flatness band. Audio wants 20 Hz–20 kHz within a dB; instrumentation wants DC precision or a defined band. Slew rate must support the highest frequency at full amplitude (V/µs = 2πfVpk ÷ 10⁶).
## How to apply this in your build
Work through the sequence below each step assumes the previous one passed. For numbers that need calculating, the linked tools at the end of this guide do the arithmetic instantly.
1. List every RC in the signal path with its corner
2. Verify each corner sits outside the band of interest
3. Check slew rate for the worst-case amplitude and frequency
4. Measure the response with a sweep, not a single tone
### Worked example
A “flat” preamp measured −3 dB at 15 Hz the input coupling cap and 10 kΩ input impedance set a 7 Hz corner per stage, two stages stacked. Doubling the cap restored inaudible bass behaviour. Run the numbers yourself with the Frequency & Wavelength and the result should agree to within rounding.
> Practical note from the bench. Every amp review on Procirel publishes the measured sweep specifications convince, sweeps demonstrate.
## Field mistakes we see again and again
– Quoting gain without a frequency band
– Stackming stages until corners creep into the passband
– Judging slew headroom by sine bandwidth instead of full-scale edges
## Key takeaways
– Poles, rolls and dB per decade the foundation of this guide. Revisit it if any measurement here surprises you.
– Feedback flattens what it can the foundation of this guide; revisit it if any measurement here surprises you.
– Specifying bandwidth honestly the foundation of this guide; revisit it if any measurement here surprises you.
## Prerequisites and preparation
Before starting: list every rc in the signal path with its corner and verify each corner sits outside the band of interest. Keep the [Frequency & Wavelength](/tools/frequency-wavelength) and [opamp-gain](/tools/opamp-gain) open every number in the worked example is reproducible. Total time including the bench steps: about 6–7 minutes.
## Who benefits most
Hobbyists meeting this topic for the first time, students who want the version with real numbers instead of abstract symbols. Returning engineers refreshing a corner of the craft. The mistake list alone justifies the visit every entry in it was learned the expensive way.
### Quick reference card
| Aspect | Where to find it in this guide |
| — | — |
| Core theory | Poles, rolls and dB per decade |
| Application steps | How to apply this in your build |
| Worked numbers | Worked example |
| Failure modes | Field mistakes we see again and again |
## How this fits the amplifiers complete guide track
This guide is one stop in the structured learning path. Start from the [amplifiers complete guide](/tutorial/amplifiers-complete-guide) pillar page for the full map, or continue with [THD measurement](/tutorial/total-harmonic-distortion-thd) and [buffering between stages](/tutorial/op-amp-voltage-follower). For the arithmetic, open the [Frequency & Wavelength](/tools/frequency-wavelength) or [opamp-gain](/tools/opamp-gain).
## Frequently asked questions
What is −3 dB, really?
Half power the conventional band edge where response has just begun to fall.
Why does my amplifier ring on square waves?
Insufficient phase margin or a capacitive load the square wave is the honest ECG.
Is there a calculator for this?
Yes the [Frequency & Wavelength](/tools/frequency-wavelength) and [opamp-gain](/tools/opamp-gain) tools run the formulas from this guide instantly, client-side, with no signup.
## Where to go next
– The complete amplifiers & audio guide: [Amplifiers & Audio complete guide](/tutorial/amplifiers-complete-guide)
– Read next: [inverting op-amp: gain, virtual ground and design](/tutorial/inverting-op-amp-configuration)
– Also in this track: [non-inverting op-amp: high-impedance gain stage](/tutorial/non-inverting-op-amp-configuration)
– Continue with: [the op-amp voltage follower: small circuit, big leverage](/tutorial/op-amp-voltage-follower)
– Calculate as you go: [op-amp gain calculator](/tools/op-amp-gain) · [power dissipation tool](/tools/electrical-power) · [gain to dB converter](/tools/opamp-gain)
– Bookmark this page against the day a measurement surprises you. Most readers return to the table and the mistake list first, and that is the correct order.
## Bench verification habits
Keep a lab notebook entry for every build in this track. The measured values, the deviations from the guide and the reason for each. Six months from now, those notes are worth more than any tutorial. They describe your bench and your components rather than a general case.
When a result here disagrees with your expectation, write down both numbers before changing anything. The gap between predicted and measured is where the real engineering lives. It is usually a tolerance, a parasitic or an assumption that was never checked.
## Formulas and checks from this guide
Verification checklist for this track: measure bias at idle before signal testing, check heatsink temperature under load. Confirm gain across frequency rather than at 1 kHz alone. Amplifiers forgive nothing at their edges.
Bookmark this page against your next build in the track. The checklist above is the same one used across 19 guides in this series.
## From our lab notebook
Across the emitter resistors at idle, no signal. Compare each output device.
Thermal drift in bias. Check the bias tracker is bolted to the heatsink and re-set per the service values.