What will happen if OP Unit gain bandwidth lower than five times of sampling clock ?

Hi, All:

When designing switched capacitor filter, the unit gain bandwidth of
operation amplifier must larger than five times of sampling frequency?
(In rule of thumb)

How does this value "five" come?

If design a unit gain bandwidth of operation amplifier is lower than
five times of sampling frequency, what will happen?

Thanks a lot!

Boki.

 

The unity gain bandwidth of an opamp describes the frequency at which the
open loop gain of the op amp decreases to 1 (unity)

If an op amp has a unity gain bandwidth of 1 MHz, then the open loop gain at
1 MHz is approximately 1. Not much good as an amplifier at that frequency.

The unity gain bandwidth is also usually equal to the Gain-Bandwidth
Product, which means that in a closed loop system the closed loop gain times
the bandwidth of the circuit equals the unity gain bandwidth. This is
usually used to ascertain the bandwidth available for a given closed loop
gain, or to find the maximum gain allowable for a specified bandwidth.

If the op-amp has a UGBW of 1 MHz, then using a factor of five times the
sampling frequency means that the sampling frequency must be less than 200
KHz. At 200 KHz the closed loop gain is limited to 5. (G*BW=UGBW; 5 *
200KHz = 1MHz.) This ensures that the op amp has enough gain to perform the
task.

If the unity gain bandwidth of the operational amplifier is lower than five
times the sampling frequency, the open loop gain (and the slew rate) of the
op amp may not be high enough to be sure of proper switching.

As you note, this is a 'rule of thumb', and is not precise, but has been
found to be a good guideline for practical use.

Good luck,
Neil Preston, CET