Real operational amplifiers (A-level only): Frequency response curve.

The idea

A frequency response curve plots the gain of an operational amplifier against the frequency of the input signal, usually on logarithmic axes. At low frequencies the gain is approximately constant at the open-loop value, then falls as frequency rises. The curve shows where gain has dropped by 3 dB from its low-frequency value; this is the bandwidth limit, and the product of gain and bandwidth is roughly constant. For a real op-amp, stray capacitance and internal compensation cause this roll-off. To obtain the curve, apply a small sinusoidal input of fixed amplitude, vary its frequency across a wide range, and measure the output amplitude with an oscilloscope or meter, calculating gain as output amplitude divided by input amplitude.

What earns the marks

• A frequency response curve shows how voltage gain varies with input signal frequency for a given op-amp configuration.
• At low frequencies the gain is approximately constant and equal to the open-loop or closed-loop value, depending on the circuit.
• As frequency increases, gain falls; the upper limit is often quoted where gain has fallen by 3 dB from its low-frequency value.
• The bandwidth is the range of frequencies over which the gain remains within 3 dB of its maximum, and it is linked to the gain by gain × bandwidth = constant.
• A practical method is to apply a fixed-amplitude sine wave, vary frequency, measure input and output amplitudes, and plot gain against frequency.
• Logarithmic axes or a Bode-style plot make the constant gain region and the roll-off easier to identify.

Common mistakes and how to put them right

• Plotting output amplitude rather than gain.

  Put it right: Divide output amplitude by input amplitude at each frequency so the curve describes the device rather than the test signal.

• Assuming the curve is flat at all frequencies.

  Put it right: Recognise the high-frequency roll-off caused by internal capacitance and compensation.

• Reading the bandwidth at the point where gain reaches zero.

  Put it right: Use the 3 dB reduction point from the low-frequency gain.

Exam tips

• Label both axes with quantity and unit, and state whether gain is a ratio or in decibels.
• When describing a measurement, specify fixed input amplitude, varied frequency, and measurement of both input and output.
• Link the shape of the curve to the gain–bandwidth relationship rather than treating it as an isolated graph.