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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: