A notch for a narrow
frequency band of a few per cent or even less normally requires
close-tolerance components. At least, that’s what we thought until we
came across a special opamp IC from Maxim.
In filters with steep slopes, the component tolerances will interact
in the complex frequency response. This effect rules out the use of
standard tolerance components if any useful result is to be achieved.
The circuit shown here relocates the issue of the value-sensitive
resistors that determine the filter response from ‘visible’ resistors to
ready available integrated circuits which also make the PCB
layout for the ﬁlter much simpler. The operational amplifiers we’ve in
mind contain laser-trimmed resistors that maintain their nominal value
within 1‰ or less. For the same accuracy, the effort that goes into
matching individual precision resistors would be far more costly and
time consuming. The desired notch (rejection) frequency is easily
calculated for both R-C sections shown in Figure 1.
Dividing the workload:
The circuit separates the amplitude and frequency domains using two
frequency-determining R-C networks and two level-determining feedback
networks of summing amplifier IC2, which suppresses the frequency
component to be eliminated from the input signal by simple phase
shifting. IC1 contains two operational amplifiers complete with a
feedback network. The MAX4075 is available in no fewer than 54 different
gain specifications ranging from 0.25 V/V to 100 V/V, or +1.25 V/V to
101 V/V when non-inverting. The suffix AD indicates that we are
employing the inverting version here (G = –1).
These ICs operate as all-pass filters producing a phase shift of
exactly 180 degrees at the roll-off frequency f0. The integrated
amplifier resistors can be trusted to introduce a gain variation of less
than 0.1 %. They are responsible for the signal level (at the notch
frequency) which is added to the input signal by IC2 by a summing
operation. However, they do not affect the notch frequency proper — that
is the domain of the two external R-C sections which, in turn, do not
affect the degree of signal suppression. In general, SMDs
(surface mount devices) have smaller production tolerance than their
leaded counter-parts. Because the two ICs in this circuit are only
available in an 8-pin SOIC enclosure anyway, it seems logical to employ SMDs
in the rest of the circuit as well. Preset P1 allows the ﬁlter to be
adjusted for maximum rejection of the unwanted frequency component.
Figure 2. This deep notch is within reach using just 5%-tolerance resistors and 20%-tolerance capacitors.
R-C notch ﬁlter:
Using standard-tolerance resistors for R1 and R2 (i.e., 1%, 0806
style) and 10%-tolerance capacitors for C1 and C2 (X7R ceramic) an
amount of rejection better than that shown in Figure 2 may be achieved.
The notch frequency proper may be defined more accurately by the use of
selected R-C sections. Pin 3 of IC2 receives a signal that’s been
90-degrees phase shifted twice at the notch frequency, while pin 1 is
fed with the input signal. These two signals are added by way of the two
on-chip resistors. IC2 is a differential precision operational
amplifier containing precision resistor networks trimmed to an error not
exceeding ±0.2‰. Here, it is configured as a modified summing amplifier
with its inverting input, pin 2, left open.
For frequencies considerably lower than the resonance frequency f0 =
1 / (2 π R C) the capacitors present a high impedance, preventing the
inverting voltage followers from phase-shifting the signal. At higher
frequencies than f0, each inverting voltage follower shifts its input
signal by 180 degrees, producing a total shift of 360 degrees which
(electrically) equals 0 degrees. The phases of each all-pass ﬁlter
behave like a simple R-C pole, hence shift the signal at the resonance
frequency by 90 degrees each. The three precision amplifier ICs can
handle signals up to 100 kHz at remarkably low distortion. The supply
voltage may be anything between 2.7 V and 5.5V. Current consumption will
be of the order of 250µA.