# System Bandwidth for Cascaded Amplifiers

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This Demonstration calculates the total system risetime and bandwidth for a series of up to six cascaded amplifiers as a function of the individual bandwidths of each amplifier. It assumes that each individual amplifier does not load or change the bandwidth of any other amplifier.

Contributed by: Allen Hollister (March 2011)

Open content licensed under CC BY-NC-SA

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## Details

The approximate total system bandwidth , for a series of cascaded wide-bandwidth amplifiers is given by the equation where through are the bandwidths of the individual amplifier stages. The units for the bandwidth sliders are controlled by the "units of frequency" button. It is assumed that each stage is independent of other stages—input impedance of each stage is infinity and the output impedance is zero. The equation is approximate, but reasonably accurate for most amplifiers. Most accuracy occurs when one amplifier is clearly the dominant pole. Worst case accuracy occurs if all amplifiers are identical in bandwidth. In this case, the most accuracy occurs when the individual amplifiers have a maximally flat envelope delay (MFED) filter response. For this special case, and with a six-amplifier system, a 3.36% error occurs. The number of actual poles within any one particular amplifier is unimportant to this equation as long as the above conditions are satisfied.

Bandwidth and risetime are approximately related by the equation , where is the bandwidth in GHz and the system risetime trs is in ns. The actual units for the system risetime are selectable using the "units of time" button. This equation is approximate and is most accurate when the system filter response is MFED. This equation can be used to calculate a bandwidth for an individual amplifier should the risetime be known instead of the amplifier bandwidth.

Reference: A. Hollister, *Wideband Amplifier Design,* Raleigh, NC: SciTech Publishing, 2007.

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