Theory of Operation

The THAT 2150 Series VCAs are designed for high

performance in audio-frequency applications requiring

exponential gain control, low distortion, wide dynamic

range and low dc bias modulation. These parts control

gain by converting an input current signal to a bipolar

logged voltage, adding a dc control voltage, and re-con-

verting the summed voltage back to a current through

a bipolar antilog circuit.

Figure 6 presents a considerably simplified internal

circuit diagram of the IC. The ac input signal current

flows in pin 1, the input pin. The internal op amp

works to maintain pin 1 at a virtual ground potential

by driving the emitters of Q1 and (through the Voltage

fined as flowing into pin 1), the op amp drives the emit-

ter of Q1 negative, turning off its collector current,

while simultaneously driving the emitter of Q3 nega-

tive, turning it on. The input signal current, therefore,

is forced to flow through Q3 and D3.

Logging & Antilogging

Because the voltage across a base-emitter junction

is logarithmic with collector current, the voltage from

the base of Q3 to the cathode of D3 is proportional to

the log of the positive input current. The voltage at the

cathodes of D3 and D4 is therefore proportional to the

log of the positive input currents plus the voltage at

pin 3, the negative control port. Mathematically,













,

kT

q

Q3. It is assumed that D3 matches Q3 (and will be as-

sumed that they match Q4 and D4, as well).

In typical applications (see Figure 3, Page 3), pin 4

is connected to a voltage source at ground or nearly

ground potential. Pin 8 is connected to a virtual

ground (usually the inverting input of an op amp with

negative feedback around it). With pin 4 near ground,

and pin 8 at virtual ground, the voltage at the cathodes

of D3 and D4 will cause an exponentially-related cur-

rent to flow in D4 and Q4, and out via pin 8. A similar

equation governs this behavior:













.

Exponential Gain Control

The similarity between the two preceeding equations

begs further exploration. Accordingly:





























































.

Rearranging terms,

.

If pin 3 and pin 4 are at ground potential, the cur-

rent in Q4/D4 will precisely mirror that in Q3/D3.

When pin 3 is positive with respect to pin 4, the voltage

across the base-emitter junction of Q3 is higher than

that across the base-emitter junction of Q4, so the

Q4/D4 current remains proportional to, but less than,

the current in Q3/D3. In the same manner, a negative

voltage at pin 3 with respect to pin 4 causes the

Q4/D4 current to be proportional to, but greater than

that in Q3/D3.

The ratio of currents is exponential with the differ-

“deci-linear” control. Mathematically, this is:

= e

For pin 4 at or very near ground, at room tempera-

ture (25˚C), allowing for a 10˚C internal temperature

rise, and converting to a base of 10 for the exponential,

this reduces to:

-

+

Q1

Q4

Q3

Q2

D3

D1

5

4

8

3

1

2

(SYM)

V-

IN

Ec+

Ec+

OUT

Ec-

Generator

Bias

Voltage

D2

D4

V3

Iin

Figure 6. Simplified Internal Circuit Diagram

THAT Corporation; 734 Forest Street; Marlborough, Massachusetts 01752; USA

Tel: (508) 229-2500; Fax: (508) 229-2590; Web: http://www.thatcorp.com

Page 4

2150 Series IC VCAs