Handbook for Sound Engineers

Consoles 881

25.11.11 The Bootstrap

The simplest fake inductor is shown in Fig. 25-63A,

with typical values. It relies on a technique called boot-

strapping. The principles are shown in Fig. 25-62. A

1k: resistor with 1 V across it will pass 1 mA. Without

changing the source potential of 1 V, the bottom end of

the resistor is tied to 0.8 V. There is 0.2 V across the

resistor, and so a current of 0.2 mA flows through the

resistor. The source (still at 1 V) sees 0.2 mA flowing

away from it, the amount of current it would expect to

see going to a 5 k: resistor value (1 V/0.2 mA = 5 k:).

It thinks it’s looking at a 5 k: resistor! Continuing this,

stuffing a potential of 1 V (not the same source) at the

bottom end of the resistor means there is no voltage

across the resistor, so there is no current flow. Our orig-

inal source thinks it’s seeing an open circuit (infinite

resistance) despite the fact that there is still a definite,

real, physical 1 k: resistor hanging on it.

This phenomenon holds true with any source
voltage, ac or dc, provided the instantaneous bootstrap
voltage is the same as the source. Any phase or potential
difference creates an instantaneous potential difference
across the resistor; current flows and an apparent resis-
tance materializes.
This fake inductor works on frequency-dependent
Figure 25-61. Totem-pole gyrators. bootstrapping, the terminal being almost totally boot-

E. Input/output response of D.

A. Totem pole gyrator with typical values.

B. High-pass filter.

C. Input output response of B.

D. Bandpass filter.

Q approximately 30

Loss indicates

dynamic impedance

@ 20 k 7

Totem pole

Totem pole

as shown

10 k 7

10 k 7

10 k 7

10 k 7

1 k 7

(C1)

0.1MF

0.1MF

100 Hz 1 kHz 10 kHz

Frequency

100 Hz 1 kHz 10 kHz

0

10 dB

20 dB

0.1MF

10 k 7

V 0

V 0

+ 40dB

+20 dB

0

10 dB

Figure 25-62. Bootstrapping analysis.

Main

terminal

Terminal sees

Zero volts

ground

No current Opencircuit

Note: 1 k 7 resistor is attached

to terminal in all cases

1 k (^7) 1 mA
1V
1 k (^7) 0.2 mA
1V
0.8 mA
1V
1 k 7
1V
5 k 7
1 k 7