Gain Bandwidth Product Calculation for Op Amp

When using an op amp to build an electronic circuit, we need to calculate the gain bandwidth product of our op amp thoroughly. There are many op amps with different properties so we need to take caution.

If an op amp produces too much gain, the bandwidth will be lower and vice versa. This is why the relation between gain and bandwidth is crucial when designing a circuit with an op amp.

Deciding on an op amp with its gain, bandwidth, and frequency response is our first objective.

Keep in mind first, we are talking about an op amp that operates in closed loop configuration. If an op amp is configured in a closed loop, its high gain can be used to ensure the flat response between gain and frequency relationship with sufficient bandwidth.

Before learning the gain bandwidth product, we need to understand first the most important property of an op amp: Frequency Response.

Frequency Response

Assume that we have an ideal op amp at the moment, its gain and bandwidth should be infinite. For a practical op amp, both its gain and bandwidth are finite or have certain values.

Observe the graph below where the X-axis is the frequency (measured in Hz) while the Y-axis is the gain (measured in dB).

Gain bandwidth product 1

As shown above, the gain of our amplifier is constant until the frequency is higher than the cutoff frequency (fc). Increasing frequency further than fc will reduce the gain of our op amp.

Cutoff Frequency and Compensation

Cutoff frequency (fc) is a boundary where the gain of an op amp is constant until the frequency is higher than the cutoff frequency, the gain is decreasing with the increasing frequency.

Typically, the cutoff frequency of an op amp will be low about 10 to 100Hz. Only when the frequency stays under the cutoff frequency, the op amp can deliver its maximum gain constantly.

Just an extra note, an op amp has an internal compensation capacitor. This will give better response when operating in higher operation rather than a sharp slope.

Without the compensation capacitor, the op amp will have multiple breakpoints before the gain becomes unity (1).

Gain bandwidth product 2

The multiple breakpoints exist because of capacitance from the load or stray. The op amp which does not have internal compensation will work more unstable at high frequency. This is why every op amp we use was built internally compensated with a capacitor.

Not only that, if compensated, the cutoff frequency of an op amp is very low when used in an open loop circuit.

The example of an op amp with an internal compensation capacitor is shown below.

Gain bandwidth product 3

The graph above gives us better understanding if an op amp has proper internal compensation. The op amp can work stability in higher frequency until it reaches unity gain.

Unity gain means our op amp has a gain of one.

The last graph above is what we call the Gain Bandwidth Product (GBP) of an op amp. The product of gain will remain constant until the gain reaches unity gain.

Keep in mind that the gain (dB) is the voltage ratio gain (AV) of the op amp. How do we clarify that the op amp has the constant Gain Bandwidth Product (GBP)? Use a simple equation as

For an example for the 10 Hz frequency,

Gain bandwidth product 4

The gain is 100 dB means we have a gain of 100,000 at 10 Hz frequency. The GBP will be 100,000 x 10 = 1 MHz.

Next example is 100 Hz where we have a gain of 80 dB.

Gain bandwidth product 5

80 dB is equal to 10,000 then our GBP will be 10,000 x 100 = 1 MHz.

Continuing until 1 MHz frequency where our gain is 0 dB (or equal to the gain of 1), our GBP will be 1 x 1,000,000 = 1 MHz.

This clarifies our graph where the op amp is able to deliver constant GBP even in higher frequency.

Gain Bandwidth Product (GBP) Calculation

Feedback on an op amp means the op amp is operated with a closed loop configuration where the output is partially used by the op amp.

With this feedback, we can control the voltage gain further with better results. We will get higher gain with the cost of bandwidth.

The graph below will show us the differences between open loop and closed loop responses.

Gain bandwidth product 6

Using the gain bandwidth product, we can easily determine the cutoff frequency of our op amp in a closed loop operation.

We can see clearly that the op amp produces constant gain of 40 dB (AV = 100) until it operates at 10 KHz. If we increase the frequency beyond 10 KHz, the gain starts decreasing. Just take a look at 100 KHz where it has gain of 20 dB or AV = 10.

Of course we can reverse our calculation if the known variable is the GBP and the gain. Say we have GBP of 1 MHz and gain of 40 dB (AV = 100), the operating frequency in closed loop configuration is 1 MHz divided by 100 and we have 10 KHz frequency.

From the simple examples above we can write our GBP equation as

GBP = Gain Bandwidth Product (Hz)
AV = voltage gain ratio
fc = cutoff frequency (Hz)

This equation is mainly used to help us determine the cutoff frequency where the op amp produces its highest gain constantly. It means that our GBP has to be sufficient to produce both high gain at high frequency.

For a simple example of the statement above, assume we need an op amp with conditions below.

Desired gain = 60 dB (AV = 1000)
Operation frequency = 10 KHZ

Our gain bandwidth product (GBP) should be at least

Keep in mind that the higher the GBP likely costs us more.

Frequently Asked Questions

What is the gain-bandwidth product formula?

The gain-bandwidth product (GBP) formula is the product of voltage gain and the frequency. If a GBP of an op amp is 1 MHz, the gain will be unity at 1 MHz frequency.

What is the gain-bandwidth product used for?

The gain-bandwidth product (GBP) is used for closed loop op amp only with a voltage feedback. This value is limited by the slew rate of that amplifier.

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