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Full changelogEngine 1.18.3

Op-Amp Gain & Bandwidth

Dividers & Interfacing

Closed-loop gain for four topologies, against the GBW and slew-rate limits.

Inputs

Ω
1 kΩ
1 kΩ to 100 kΩ suits most stages
Ω
10 kΩ
V
100 mV
Hz
100 kHz
Hz
10 MHz
V/µs
V
1 mV
A
10 nA
V

Results

1 passed
Closed-loop gain Av

20.83 dB (1 + Rf/R1)
11.0000V/V
Pass

Checked: f = 100 kHz against f-3dB = GBW/NG = 909.1 kHz: pass below 181.8 kHz (gain within 2 %), fail above f-3dB (3 dB down).
−3 dB bandwidth f−3dB
909.1kHz
Output amplitude Vout
1.1V
All results (4)
Noise gain NG

sets bandwidth, offset gain and stability
11.000V/V
Full-power bandwidth

slew limit at 1.1 V peak
1.447MHz
DC output error

offset × noise gain, plus bias current
± 11mV
Input impedance
≈ ∞ (op-ampinput)
Closed-loop bandwidth 909.1 kHz is 9× the signal frequency.

The inputs follow the signal, so check the op-amp's input common-mode range, especially near the negative rail on a single supply.

Op-amp open loop (GBW)Closed loop

Accuracy

Verified against

3 independent cases. See the working.

This is a design aid. The engineer remains responsible for the design and for checking the standard itself.

Parameter sweep

Vary one input over a range and see the answer and verdict at each step, as a table and a curve.Pro

Worst-case corners

Put a tolerance on each input and get the worst-case band around the answer.Pro

Parts that track move together.Inputs in the same group move together, like a matched pair or parts from one reel. Leave independent parts ungrouped: that is the safe choice.

Circuit

The principle

With negative feedback, the op-amp drives its two inputs to the same voltage, and the resistors set the gain. What limits a real stage is the noise gain, the gain-bandwidth product and the slew rate.

Non-inverting
Av=1+RfR1A_v = 1 + \frac{R_f}{R_1}
Very high input impedance; gain is at least 1.
Inverting
Av=−RfR1A_v = -\frac{R_f}{R_1}
Input impedance is R₁. The inputs stay at the reference, so there is no common-mode swing.
Noise gain (what the feedback loop sees)
NG=1+RfR1NG = 1 + \frac{R_f}{R_1}
Bandwidth, offset and stability follow NG, not the signal gain: an inverting ×1 stage has NG = 2.
Closed-loop bandwidth
f−3dB=GBWNGf_{-3dB} = \frac{GBW}{NG}
Slew-rate (full-power) limit
fmax=SR2πVpkf_{max} = \frac{SR}{2\pi V_{pk}}
A large signal can hit the slew limit well below f−3dB. Check both.
Output DC error
Verr=NG⋅Vos+IBReqV_{err} = NG \cdot V_{os} + I_B R_{eq}
  • AvA_vclosed-loop signal gain
  • NGNGnoise gain = 1 + Rf/R1
  • GBWGBWgain-bandwidth product of the op-amp
  • SRSRslew rate, V/µs
  • VpkV_{pk}peak output amplitude
  • VosV_{os}input offset voltage
  • IBI_Binput bias current
More detail

Split the gain

Two ×10 stages on the same op-amp give about six times the bandwidth of one ×100 stage. If GBW/NG is close to your signal frequency, cascade.
Further reading: TI SLOA011; Analog Devices tutorials MT-033 and MT-047.

Engine version ⁨1.18.3⁩