Tapped Tank Circuits

Operation at resonance:

X1 + X2 + X3 = 0

Qu(tap) >20 (5% error)

Capacitive Tap

Reactive Voltage Divider

32

1 2 3v

Xv

v X X

Reactive Taps

32

1 2 3

2

2 3v

Xv

v X X

C

C C

Capacitive tap

Inductive tap

32

1 2 3

3

2 3v

Xv

v X X

L

L L

Autotransformer

2 2

1 1 2v

v n

v n n

Impedance Transformation

For lossless reactive components and moderate Q, a tapped tank circuit acts exactly like a transformer:

2load

inv

ZZ

a The impedance ratio is

equal to the voltage ratio squared.

Error Analysis

A rigorous analysis of the tapped tank circuit yields: 2

1lin t

RZ jX

1

uQ

Approximation

Error Term

The fractional error is:

For a given Qu, the fractional error is maximum (worst case) when = 0, thus

MAX

1

uQ

Note that the real part is given exactly by the voltage ratio (transformer) approximation, and the error term is a pure reactance, imparting a small phase shift.

If Qu = 20, the worst case fractional error is 5%.

Impedance Transformation

As with a transformer, the transformation is bidirectional: