Rohde & Schwarz 1145.1010.04/05/06, Operating Manual

Page: 199 / 813

R&S
®
ZVA/ZVB/ZVT Trace Menu
1145.1084.12 4.37 E-6
Mathematical relations: Delay, Aperture, Electrical Length
The group delay is defined as:
where
rad/deg
= Phase response in radians or degrees
= Frequency/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 f and determining the corresponding phase change
.
The delay is thus
computed as:
The aperture f must be adjusted to the conditions of the measurement.
If the delay is constant over the considered frequency range (non-dispersive DUT, e.g. a cable), then
g
and
g,meas
are identical and
where t is the propagation time of the wave across the DUT, which often can be expressed in terms of
its mechanical length L
mech
, the permittivity , and the velocity of light c. The product of L
mech
.
sqrt( ) is
termed the electrical length of the DUT and is always larger or equal than the mechanical length ( > 1
for all dielectrics and = 1 for the vacuum).
Application: Transmission measurements, especially with the purpose of investigating deviations from
linear phase response and phase distortions. To obtain the delay a frequency sweep must be active.
The cables connecting the analyzer test ports to the DUT introduce an unwanted delay, which
often can be assumed to be constant. Use the Zero Delay at Marker function, define a numeric length
Offset or use the Auto Length function to mathematically compensate for this effect in the measurement
results. To compensate for a frequency-dependent delay in the test setup, a system error correction is
required.
Remote control: CALCulate<Ch->Tr>:FORMat DELay
Aperture
Sets a sets a delay aperture for the delay calculation. The aperture f is entered as an integer number
of Aperture Steps:
The analyzer calculates the aperture from the sweep points of the current frequency sweep.