Designing for a value of Q

As mentioned on the configuration pages, there is a

proportional relationship between the ratio of R4 and R3,

and Q.

Q

R4

R3

∝

These resistors define the gain of an inverting amplifier

that determines the peak value of gain and therefore the

Q of the filter, as Q is described as;

Q

=

Fo

3dBBandwidth

−

This value of required gain is quite critical. As the

maximum value of Q is approached, too much gain will

cause the filter to oscillate at the centre frequency Fo. A

small reduction of gain will cause the value of Q to fall

significantly. Therefore, for high values of Q factor or

tight tolerances of lower values of Q, the resistor ratio

must be trimmed.

Frequency dependant effects must be accounted for in

determining the appropriate gain. As the frequency

increases, the effective circuit gain reduces. The required

gain is nominally two but at higher frequencies it will

need to be slightly greater than two in order to

compensate for loss of gain and internal phase shifts.

This is not really a problem for circuits where the desired

Fo remains constant, as the phase shifts are accounted

for permanently. For designs where Q is high and Fo is

to be ‘swept’, care must be taken that a gain appropriate

at the highest frequency does not cause oscillation at the

lowest.

Variation in Q increases from device to device, as the

value of Q increases, due to internal gain spreads.

ZXF103

ISSUE 1 - APRIL 2002

6