AQA · A-Level · Physics

    Course version: 7408 · Version from Sept 2016

    Gain × bandwidth = constant for a given device.

    Full specification wording

    Real operational amplifiers (A-level only): gain × bandwidth = constant for a given device.

    For a given operational amplifier, the product of voltage gain and bandwidth is approximately constant.

    Checked against the AQA 7408 specification (opens in a new tab) on .

    • Point 3 of 3
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    For a given operational amplifier, the product of voltage gain and bandwidth is approximately constant. This means that if you increase the closed-loop gain by reducing negative feedback, the bandwidth over which that gain is maintained becomes proportionally smaller, and vice versa. The constant is set by the device's gain–bandwidth product, often quoted in hertz. For example, an op-amp with a gain–bandwidth product of 1 × 10⁶ Hz gives a gain of 100 up to about 1 × 10⁴ Hz, or a gain of 10 up to about 1 × 10⁵ Hz. The relationship applies while the amplifier is operating within its linear region and is a useful design trade-off between amplification and frequency range.

    What earns the marks

    • The gain–bandwidth product is approximately constant for a given op-amp device.
    • Increasing closed-loop gain reduces the available bandwidth in proportion.
    • The constant may be found from the open-loop gain and the frequency at which gain has fallen by 3 dB.
    • The relationship allows the bandwidth to be predicted for a chosen gain, or the gain to be predicted for a required bandwidth.
    • The product is valid while the op-amp remains within its linear operating region and is not slew-rate limited.
    • Typical units are hertz, since gain is a dimensionless ratio and bandwidth is a frequency.

    Common mistakes and how to put them right

    • Adding gains and bandwidths instead of multiplying.

      Put it right: Use the product gain × bandwidth and keep it constant.

    • Treating the constant as applying to all op-amps.

      Put it right: Recognise that each device has its own gain–bandwidth product.

    • Using the signal frequency rather than the bandwidth limit.

      Put it right: Identify the bandwidth as the range up to the 3 dB point.

    Exam tips

    • Write the relationship as gain × bandwidth = constant before substituting values.
    • Check that the calculated bandwidth is a frequency and give the unit hertz.
    • Use the relationship to compare two configurations of the same op-amp rather than comparing different devices.

    Try the lesson

    The start of the Real operational amplifiers (A-level only): gain × bandwidth = constant for a given device. lesson, made from checked teaching notes for this specification point.

    Have a go first

    For a given operational amplifier, the product of gain and bandwidth is constant. If the gain is increased, what happens to the bandwidth?

    Listen

    For a given operational amplifier, the product of voltage gain and bandwidth is approximately constant. This means that if you increase the closed-loop gain by reducing negative feedback, the bandwidth over which that gain is maintained becomes proportionally smaller, and vice versa. The constant is set by the device's gain–bandwidth product, often quoted in hertz. For example, an op-amp with a gain–bandwidth product of 1 × 10⁶ Hz gives a gain of 100 up to about 1 × 10⁴ Hz, or a gain of 10 up to about 1 × 10⁵ Hz. The relationship applies while the amplifier is operating within its linear region and is a useful design trade-off between amplification and frequency range. A strong answer earns marks for these points. The gain–bandwidth product is approximately constant for a given op-amp device. Increasing closed-loop gain reduces the available bandwidth in proportion. The constant may be found from the open-loop gain and the frequency at which gain has fallen by 3 dB. The relationship allows the bandwidth to be predicted for a chosen gain, or the gain to be predicted for a required bandwidth. A common slip: Adding gains and bandwidths instead of multiplying. Instead, use the product gain × bandwidth and keep it constant. Exam tip: Write the relationship as gain × bandwidth = constant before substituting values.

    See it

    A flowchart starting from the statement that gain multiplied by bandwidth is constant for a given device. From this, one branch leads to increasing the closed-loop gain by reducing negative feedback, which leads to the bandwidth becoming proportionally smaller. A second branch leads to decreasing the closed-loop gain, which leads to the bandwidth becoming proportionally larger. A third branch notes that the constant is set by the device's gain–bandwidth product, which leads to the condition that the relationship applies within the linear region, and then to the condition that the amplifier is not slew-rate limited.
    It shows that for a given op-amp the gain–bandwidth product stays constant, so raising the gain reduces the bandwidth and lowering the gain increases it, within the linear region.

    Key words

    Say what each word means before you turn the card.

    Gain and bandwidth

    Try answering aloud or in your head before turning the card.

    Operational amplifier design trade-offs

    Try answering aloud or in your head before turning the card.

    Quantitative prediction

    Try answering aloud or in your head before turning the card.

    Frequency response

    Try answering aloud or in your head before turning the card.

    See every definition
    Gain and bandwidth
    For a given device, the product of voltage gain and bandwidth is approximately constant.
    Operational amplifier design trade-offs
    Increasing the closed-loop gain by reducing negative feedback makes the bandwidth over which that gain is maintained proportionally smaller, and vice versa.
    Quantitative prediction
    The relationship allows the bandwidth to be predicted for a chosen gain, or the gain to be predicted for a required bandwidth.
    Frequency response
    The bandwidth is the range up to the 3 dB point, and typical units are hertz since gain is a dimensionless ratio and bandwidth is a frequency.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A flowchart starting from the statement that gain multiplied by bandwidth is constant for a given device. From this, one branch leads to increasing the closed-loop gain by reducing negative feedback, which leads to the bandwidth becoming proportionally smaller. A second branch leads to decreasing the closed-loop gain, which leads to the bandwidth becoming proportionally larger. A third branch notes that the constant is set by the device's gain–bandwidth product, which leads to the condition that the relationship applies within the linear region, and then to the condition that the amplifier is not slew-rate limited.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

    There is more to this lesson

    The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.

    Carry on with the full lesson

    A week of Premium from your first lesson · Then the free plan continues · No card, no charge

    Test your understanding of Real operational amplifiers (A-level only): gain × bandwidth = constant for a given device.

    Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.

    Take topic quiz

    A week of Premium from your first lesson · Then the free plan continues · No card, no charge

    Start free

    Cookies on MasteryMind

    Essential cookies keep you signed in.

    Analytics and advertising cookies stay off unless you accept.

    Read our Privacy Policy.