Gain Bandwidth Product (GBP)

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When you're using operational amplifiers (op-amps) or other linear amplifiers, there's a crucial parameter you should understand: the Gain Bandwidth Product (GBP). It's the relatively constant product of an amplifier's gain and its bandwidth, and it's a fundamental concept for a solid intuition in electronics.


For any linear amplifier, your chosen voltage gain (G) will dictate the corresponding operational bandwidth (W). This relationship is fixed by the amplifier's constant GBP. The formula is simple:

G x W = GBP

The first image shows a typical curve for an amplifier's GBP. You'll notice the gain decreases steadily as the frequency increases. This is a deliberate design choice called frequency compensation, and it's what keeps the amplifier stable. Most linear amplifiers, including op-amps, achieve this with a Miller capacitor inside the circuit, which creates a single dominant pole in the transfer function. This design gives the amplifier a consistent gain-roll-off of about -20 dB per decade, meaning the gain is reduced by a factor of 10 for every tenfold increase in frequency. This pole is created by a Miller capacitor, which is typically deliberately installed in the transconductance subsystem to prevent oscillation at the -3dB response point. (Note that not all op-amps have an internal Miller capacitor, especially very high-speed op-amps. For these, a terminal is provided for installing external Miller capacitors, allowing you to select the desired value.)


A Practical Example: The LT1128 Op-Amp

Let's look at a real-world example using the Analog Devices LT1128/LT1028. Looking at its datasheet, we find the Unity-Gain Bandwidth (GBW) is specified as 14 MHz. This means that when the amplifier is configured for a gain of 1x (or 0 dB), its bandwidth is 14 MHz. The GBW is often used as the standard value for an op-amp's GBP.


Now, let's say you're building a system with a gain of 40 dB (or 100x). We can easily calculate the new bandwidth using the GBP:

  • BW = GBP / GAIN$
  • BW = 14,000,000 Hz / 100
  • BW = 140,000 Hz or 140 kHz

Conversely, if you need a maximum bandwidth of 14 kHz, you can calculate the maximum gain you can achieve:

  • GAIN = GBP / BW
  • GAIN = 14,000,000 Hz / 14,000 Hz
  • GAIN = 1000 or 60 dB


The Reality of Non-Ideal Components

While the math above is correct in theory, real-world circuits are never perfect. As the LT1128 graph shows, at unity gain (1x), the actual bandwidth might only be around 7-8 MHz, not the theoretical 14 MHz. This discrepancy highlights the importance of real-world factors.

The GBP model assumes an ideal roll-off, but in practice, slew rate limitations and other non-ideal behaviors can limit the amplifier's ability to produce a clean signal at higher frequencies, especially with larger signal amplitudes. This often reduces the usable bandwidth below the theoretical GBP value.

This is where the true "art of electronics" comes in. The theoretical calculations give us a great starting point, but a good designer always accounts for these real-world imperfections. Don't rely solely on paper calculations—always prototype and test your designs to ensure they perform as needed.


(This post is parallel to the status on the FaceBookGroup The Art of Electronics with the same topic)



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