R&S ZNC3, Руководство пользователя

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Concepts and Features
R&S
®
ZNC
58 User Manual 1173.9557.02 ─ 13
| | | ) ( |
| | 1
:
21 12 21 12 22 11 11 22
2
11
1
S S S S S S S S
S
      



| | | ) ( |
| | 1
:
21 12 21 12 22 11 22 11
2
22
2
S S S S S S S S
S
      



where denotes the complex conjugate of S.
Stability factors are calculated as functions of the frequency or another stimulus param-
eter. They provide criteria for linear stability of two-ports such as amplifiers. A linear circuit
is said to be unconditionally stable if no combination of passive source or load can cause
the circuit to oscillate.
●
The K-factor provides a necessary condition for unconditional stability: A circuit is
unconditionally stable if K>1 and an additional condition is met. The additional con-
dition can be tested by means of the stability factors μ
1
and μ
2
.
●
The μ
1
and μ
2
factors both provide a necessary and sufficient condition for uncondi-
tional stability: The conditions μ
1
>1 or μ
2
>1 are both equivalent to unconditional sta-
bility. This means that μ
1
and μ
2
provide direct insight into the degree of stability or
potential instability of linear circuits.
References: Marion Lee Edwards and Jeffrey H. Sinsky, "A New Criterion for Linear 2-
Port Stability Using a Single Geometrically Derived Parameter", IEEE Trans. MTT, vol.
40, No. 12, pp. 2303-2311, Dec. 1992.
3.3.7 Delay, Aperture, Electrical Length
The group delay τ
g
represents the propagation time of wave through a device. τ
g
is a real
quantity and is calculated as the negative of the derivative of its phase response. A non-
dispersive DUT shows a linear phase response, which produces a constant delay (a
constant ratio of phase difference to frequency difference).
The group delay is defined as:
df
d
d
d
deg
rad
g

   
360




where
Φ
rad
, Φ
deg
= phase response in radians or degrees
ω = angular velocity in radians/s
f = frequency in Hz
In practice, the analyzer calculates an approximation to the derivative of the phase
response, taking a small frequency interval Δf and determining the corresponding phase
change ΔΦ. The delay is thus computed as:
Measurement Results