R&S ZNB Series User Manual page 143

®
R&S ZNB/ZNBT
Stability factors are calculated as functions of the frequency or another stimulus
parameter. They provide criteria for linear stability of two-ports such as amplifiers. A lin-
ear 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 with the stability factors μ
●
The μ
tional stability: The conditions μ
stability. This means that μ
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.
4.3.8 Group delay
The group delay τ
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:


g
where
Φ , Φ
rad
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 group delay is computed as

g , meas
where ΔΦ/Δf is the slope of the regression line through the frequency points of aper-
ture Δf.
Δf must be adjusted to the conditions of the measurement, e.g. it must be reduced if
phase slope fluctuates significantly over frequency. Otherwise group delay variations
are flattened out.
Note that the input value "Aperture Points" does not define the number of frequency
points, but the number of frequency steps between the points. I.e. "Aperture Points" is
User Manual 1173.9163.02 ─ 62
and μ factors both provide a necessary and sufficient condition for uncondi-
1 2
represents the propagation time of wave through a device. τ
g


d
d
   deg
rad


d 360 df
= phase response in radians or degrees
deg


  deg
  
360 f
and μ
1
>1 or μ >1 are both equivalent to unconditional
1 2
and μ provide direct insight into the degree of stability
1 2
Concepts and features
Measurement results
.
2
is a
g
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