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All-Pass Network, Second-Order(AP2)

All-Pass Network, Second-Order(AP2)

Properties	Description	Unit	Default	Range
R	Image impedance	Ohm	Required	³ 0
F	Resonant frequency	Hz	Required	³ 0
M	Shape factor	None	Required	³ 0
Q	Quality factor	None	¥	> 0

Notes

1. The model is described by the following:

where RI is the image impedance, and corresponds to R in the table of parameters, and F₀ is the resonant frequency, and corresponds to F in the table of parameters.

2. AP1 is useful for finding values of M, F (F₀), and possibly R (RI) through optimization.

3. The quality factor Q is assumed to be infinite (R_d=0 W) unless a nonzero positive value is supplied.

4. The lattice impedances of the second-order all-pass network are:

_,

_,

where:

where f is the frequency.

In terms of the AP2 parameters:

_.

5. There are a number of implementations depending on the value of M [Refs. 1 and 2], three of which are given below. Implementation No. 1 (0<M<¥)

_,

_,

, and

_.

6. Implementation No. 2 (0<M£1)

_,

_,

, and

_.

7. Implementation No. 3 (1£M£Ö2)

_,

_,

_,

, and

_.

Netlist Form

AP2:NAME n1 [n2] [n3] [n4] R=val F=val M=val [Q=val]

Netlist Example

Quality factor ¥:

AP2:APQI 1 2 R=500 F=1MHZ M=1

Quality factor 50:

AP1:APQ50 1 2 R=500 F=1MHZ Q=50

References

1. H. Matthes, “Designing High-grade Delay Equalizers,” NTZ-CJ, No. 4, pp. 177-185; 1965.

2. Vernon R. Cunningham, “Design Single-Section Delay Equalizers,” Electron Design, Vol. 19, pp. 82-87; Sep. 13, 1976.

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