Handbook for Sound Engineers

Tubes, Discrete Solid State Devices, and Integrated Circuits 343

(12-60)

where,

K varies between 0 and 1 as the control voltage is
changed from full attenuation to full gain.

When the control voltage is 0 V, K= 0.5 and both
output voltages equal the input voltage. The value K is
exponentially proportional to the applied control
voltage; in the SSM2018T, the gain control constant in
the basic VCA configuration is 30 mV/dB, so the
decibel gain is directly proportional to the applied
control voltage. This makes the part especially appli-
cable to audio applications.

The SSM2018 has many applications as a VCA, but
its use as a voltage-controlled panner (VCP) is perhaps
one of the most unique, Fig. 12-43.

THAT Corporation’s 2180 and 2181 VCAs. The
Blackmer VCAs now offered by THAT Corporation
(which registered the trademark “Blackmer” for this
application) exploit the mathematical property that
adding a constant to the logarithm of a number is equiv-
alent, in the linear domain, to multiplying the number
by the antilog of the constant.

The equation for determining the output is

(12-61)

Iin is multiplied by the antilog of EC to produce Iout.
Conveniently, and fortunately for Blackmer, the expo-
nential response of EC is linear in dB.

Consider the unity-gain case when EC=0.

Blackmer VCAs exploit the logarithmic properties of

a bipolar junction transistor (BJT). In the basic

Blackmer circuit, the input signal Iin (the Blackmer

VCA works in the current, not the voltage domain) is

first converted to its log-domain equivalent. A control

voltage, EC, is added to the log of the input signal.

Finally, the antilog is taken of the sum to provide an

output signal Iout. This multiplies Iin by a control

constant, EC. When needed, the input signal voltage is

converted to a current via an input resistor, and the

output signal current is converted back to a voltage via

an op-amp and feedback resistor.

Like the Frey OVCE, the Blackmer VCA’s control

voltage (EC) is exponentiated in the process. This makes

the control law exponential, or linear in dB. Many of the

early embodiments of VCAs for electronic music were

based on linear multiplication and required exponential

converters, either external or internal to the VCA, to

obtain this desirable characteristic.^15 Fig. 12-44 shows

the relationship between gain and EC for a Blackmer

VCA.

Audio signals are of both polarities; that is, the sign

of Iin in the above equations will be either positive or

negative at different times. Mathematically, the log of a

negative number is undefined, so the circuit must be

designed to handle both polarities. The essence of

David Blackmer’s invention was to handle each

phase—positive and negative—of the signal waveform

Figure 12-43. SSM2018 as a VCP. Courtesy Analog
Devices, Inc.

Vout 2 = V 1 – G

= 21 – K uVin

Vin

Vc

VG

V 1 G

18 k 7

18 k 7

Iout=antilog>@ logIin+EC

=Iinu>@antilogEC

Figure 12-44. THAT 2180 gain versus EC+. Courtesy THAT

Corporation.

Iout=antilog>@ logIin 0+

=Iinu>@antilog 0

=Iinu 1

Iout=Iin

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  Ec+—mV