
ZXF36L01
ISSUE 3 - JANUARY 2002
8
DESIGNING FOR A VALUE OF Q
As menti
oned on the configuration pages, there is a
proportional, but non-linear relationship between the
ratio of Rf and Ri, and Q.
These resistors define the gain of an inverting amplifier
that determines the peak value gain and therefore the Q
of the filter,Q is defined as:
Q
f
dB Bandwidth
O
=
3
This value of required gain is 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 or tight
tolerances of lower values of Q, the resistor ratio must
be trimmed as shown.
Frequency dependant effects must be accounted for in
determining the appropriate gain. As the frequency
increases because of internal phase shift effects the
effectivecircuitgainreducesandthus QFactorreduces.
The frequency effect is not a problem for circuits where
the 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.
Suggestion for gain setting component values.
several example conditions:
Example1
fo = 48kHz,
R = 10k
, C = 320pF
Rf/Ri = 36.6k
/ 18 k
=> 2.033
Q=60,
Example2
fo = 140kHz,
R = 10k
, C = 100pF
Rf/Ri = 37k
/ 18k
=> 2.055
Q=15,
It can be seen from these examples that the higher Q
exampleactuallyhasalowerinvertingamplifiergain.
As mentioned before, the frequency will affect the
value of gain. The Q Factor v Frequency graph
illustrates this effect.
These examples show that the gain required is
nominally 2. For the specified range of Q: 0.5 to 50
(valuesupto250areobtainable),thegainvaluesvary
from 1.9 to 2.5 correspondingly.
Due to internal gain errors, when the absolute value
of Q is increased, the device to device variation in Q
will also increase.
Pin 11
Pin 9
22k
2k
10k
Pin 10
This diagram shows the exponential relationship between gain and Q Factor. (fo = 140 kHz)