Handbook for Sound Engineers

878 Chapter 25

frequency at which the curve departs significantly from
flat.
Standard arithmetic formulas normally consider or
obtain a frequency at which the curve has departed 3 dB
from flat (the 3 dB down point) being usually also
where the phase has been shifted 45°. This is only
partially useful in the design of filters for use in prac-
tical EQs; the departure point, or turnover frequency, is
generally more relevant.

25.11.3 Changing Filter Frequency

With any of these filters, moving the frequency at which
the filter bites can be achieved by altering any of the R,
L, or C values. Making any value smaller moves the
frequency higher, while making the value larger moves
the frequency lower.
There are an endless number of combinations of
element values to create the same curve at the same
frequency. In Fig. 25-58A if the value of the capacitor
were reduced (increased in reactance), the filter curve
would shift up in frequency. A corresponding propor-
tional increase in the series resistor value would result
in the original turnover frequency being restored; we
have an identical filter with a different resistor/reactor
combination. What does remain the same is the ratio or
relationship between the two elements. It is only the
filter impedance (the combination of resistance and
reactance) that varies.
With the exception of a few, the operation of any
active filter can eventually be explained by referring to
these basic single-order filter characteristics in Fig.
25-58.
There is one particular combination of two reactive
elements (capacitance and inductance) that is of prime
relevance to the construction of EQs. This, a
series-tuned circuit, Fig. 25-59, is where things really
become interesting.

25.11.4 25.11.4 Reactance and Phase Shifts

In, for example, the context of a simple resistor/reactor
filter (Fig. 25-58A), the reactance not only causes an
amplitude shift with frequency but also a related phase
shift. A fundamental difference between the two types
of reactance (C and L) is the direction of the output
voltage (Vo) phase shift with respect to the source (Vin).
More specifically, the capacitor in Fig. 25-58A causes
the output voltage phase to lag farther behind the input
as the roll-off progressively bites to a limit of 90° at
the maximum roll-off of the curve, while the inductor of
Fig. 25-58C imposes an increasing voltage phase-lead

as the low-frequency roll-off descends with a limit of

+90° at maximum attenuation.

The two reactances, in their pure forms, effect phase

shifts of +90° to 90° to an ultimate extent of 180°

opposed; they are in exact opposition and out of phase

with each other.

Figure 25-59. Series resonant circuits.

D. Responses in C for different reactances:

effect on filter bandwidth.

A. Series inductor

and capacitor:

series tuned circuit. B. Simplified reactance

plots for A.

C. Notch filter: effects shown in D.

Vo

C

L

Vin

C

B

A A

Higher

reactances

B

Resonance

C

L

Reactance

Capacitive

Inductive

Combined

reactive

values

Resonance

Frequency

R

Vo

3 dB

point

Relative bandwidths at 3 dB point

Frequency

C

A

D D

Lower

reactances

B

C

D