accurate, reliable, and useful measurements of RF power in the forward (transmission) and reverse (reflection) directions
requires careful selection of test devices and detection equipment. LadyBug Technologies has produced a white paper
describing a method for performing reflection and transmission measurements using a power sensor and a directional
coupler. It includes a discussion on coupler directivity and impedance match as a factor in measurement accuracy.
A scalar network analyzer is a low cost easy to use solution for making reflection and transmission measurements.
This paper is devoted to the hardware required to configure a reflection/transmission test setup and methods for
making quality reflection and transmission measurements, including calibration.
Reflection Scalar Analyzer Block Diagram
The reflection scalar network analyzer solution is used for making reflection measurements on a port of
a DUT (Device Under Test). In the solution above the RF source is connected to a Forward and Reflected signal
separation device (Reflectometer). The DUT is connected to the output of the Reflected Signal Separation Device.
The Signal Separation Devices are oriented to couple the forward and reflected signals as shown. The
coupled arms of each signal separation device are connected to an LB4XXA Power Sensor being used as the detector.
The Ladybug Technologies LB4XXA PowerSensor+ are ideal for this application because they offer:
Signal separation device selection:
- Easy to integrate ATE software components.
- Fast 2000 settled points/second enabling real time measurements
- Wide -60 dBm to +20 dBm dynamic range
The signal separation device is often a coupler. Consideration
should be given to the coupler’s directivity and match. Usually directivity dominates measurement error.
However, as the DUT’s return loss becomes smaller match becomes a more significant contributor. Table 1 provides
coupler directivity and match given a DUT’s return loss and worst case error. Worst case error assumes an
open short tracking calibration has been done.
Example 1: Determine coupler specifications
for a DUT with (expected) return loss of 15 dB and a total worst
case error of 40%.
Solution 1: Use coupler specifications for 40% and 16 dB worst case
error: Coupler directivity = 26 dB and
coupler match = 19 dB. Further, maximize measurement dynamic range by selecting a coupler
with 10 dB coupling factor.
If avoiding calibration is desired match the forward and reflected couplers, minimizing their insertion
loss. Also minimize adaptors and cabling between the couplers and the DUT. Unless DUT match is less
than 10 dB a dual directional coupler is not recommended because of poor resulting directivity (even if the coupler
has reasonably good directivity). The tracking error is approximately twice the insertion loss of the coupler
and cabling between the reflected coupler and the DUT. Approximate worst case error is found by adding this
tracking error to the error shown in the table.
Example 2: Determine the additional error
in Example 1 if a tracking calibration is not done.
Solution 2: Typical insertion loss
for a 10 dB coupling factor coupler is 0.5 dB. Assume cable loss between
the coupler and DUT is 0.1 dB. This additional error or tracking error is
1.2 dB (0.5 dB X 2 + 0.1 dB X2).
Alternatively the tracking error can be estimated (or measured by calibrating)
and removed from the result. Because tracking error is a loss, the resulting match measurement is simply offset
by the estimated tracking error. Add the tracking error to the match measurement.
3: Assume a 17.1 dB measurement result and Example 2 configuration. Determine the match
result given the tracking error offset.
Solution 3: 15.9 dB. Add the 1.2 dB tracking
error to the 17.1 dB match measurement.
The forward signal separation device may be replaced with a two resistor
power splitter, such as a Picosecond Pulse Labs 5336 or an Agilent 11667A. The splitter offers good broadband
performance however lacks in its ability to handle high power.
Maximizing Dynamic Range:
noted in Example 1 dynamic range should be considered. In general dynamic range is maximized by:
- Using low coupling factors. In general default to using a 10 dB (coupling factor) coupler.
- Maximize RF source power. Keeping it within the range of the power sensors being used. As source power
begins to exceed 1/2 watt, Increase coupler coupling factor.
- Select power sensors with maximum measurement speed throughout its dynamic range. Such as the LadyBug
Technologies LB4XXA PowerSensor+ that can measure 2000 settled points per second at - 60 dBm.
Reflection/Transmission Scalar Analyzer Block Diagram
By adding a third LBXXA Power Sensor transmission measurements (S21 or S12) can be made. Port match
of the power sensor and of the reflectometer in combination with DUT’s S parameters determine errors in measuring
the DUTs S21 or S12. Measurement error for a DUT with S21 = S12 = 0 dB is typically 0.27 dB (DUT match = 15
dB, Power Sensor match = 27 dB, reflectometer match = 19 dB). Increasing DUT S21 and S12 can reduce this error
to 0.22 dB; this error would begin to rise when considerations for dynamic range are included.
Mathematics of the correction is considered in this section. It is assumed the user has the expertise
to apply the programming examples provided in the LadyBug product literature to set up and read power measurements
from the LB4XXA Power Sensor and apply those measurements to the equations below.
The basic measurement equations can be done in either linear or dB. Both are presented
below. In dB form power measurements in dBm can be used directly. In linear form the square root of
linear power must be taken.
Linear form of the solution
Reflected match is
ρ is the liner reflection coefficient of the
τ is the liner tracking correction
between the forward and reflected signals;
b is the linear measured reflected square root of power;
a is the
linear measured forward square root of power.
All that remains is to determine the correct value of the
objective of the calibration is to measure τ
. τ is computed from the measurement
of two calibration standards, an open and a short. Removal of the source match error from
τ is accomplished by ensuring the open and
short are balanced and that their reflection coefficients are 180 degrees apart.
Measurement of the open
= |1| = τO (bO/aO),
τO = (aO/bO).
= |1| is the liner magnitude reflection coefficient for an ideal open;
τO is the liner tracking measurement
for the open calibration;
bO is the linear measured reflected square root of power for the open calibration;
aO is the linear measured forward square root of power for the open calibration.
the short is
ρS = |-1| =
τS = (aS/bS).
ρS = |-1| is
the liner magnitude reflection coefficient for an ideal short;
τS is the liner tracking measurement
for the short calibration;
bS is the linear measured reflected square root of power for the short
aS is the linear measured forward square root of power for the short calibration.
Determine τ by averaging
τ = (τO
It should be noted
the either τO or
τS may be used for
τ; however the error associated with source
match for the final result will increase. This additional error may be as high as 0.4 to 0.5 dB. If
this trade off is acceptable, it would be worthwhile considering the use of 20 dB couplers and minimize the uncorrected
crosstalk and avoid a calibration all together.
Example 4: Use 20 dB couplers in Example
2 and determine the approximate tracking.
Solution 4: Typical insertion loss for
a 20 dB coupler is 0.12 dB. The resulting tracking error offset would
be 0.44 dB (0.12 dB x 2 + 0.1 dB x 2).
Form of the solution in dB.
Return Loss is:
RL = ρdB =
τdB + bdB - adB.
RL = ρdB is the
return loss of the DUT;
the tracking correction in dB;
bdB is the reflected power measurement in dBm;
the forward power measurement in dBm.
Reflection Tracking Calibration:
Measurement of the open
in dB is
RLO = ρdBO
= τdBO + bdBO - adBO,
τdBO = adBO
= 0 is the return loss for an ideal open;
τO is the tracking measurement in
dB for the open calibration;
bO is the reflected power measurement in dBm for the open calibration;
aO is the forward power measurement in dBm for the open calibration.
Measurement of the short
in dB is
RLS = ρdBS
= τdBS + bdBS - adBS,
τdBS = adBS
= 0 is the return loss for an ideal short;
the tracking measurement in dB for the short calibration;
bS is the reflected power measurement in
dBm for the short calibration;
aS is the forward power measurement in dBm for the short calibration.
Determine τ by taking the linear average
of τO and
τ = 20 x Log10( 10^(-τO/20)
Measurement and Correction:
Both the linear and dB form of the measurement equation is presented below. In
dB form power measurements in dBm can be used directly. In linear from the square root of linear power must
be taken before application of the equations.
Linear form of the solution
gain or loss is
L = ττ (c/a).
L is the liner transmission gain or loss of the DUT;
ττ is the linear transmission
c is the linear measured transmitted square root of power;
a is the linear measured forward
square root of power.
Measurement of ττ
The objective of the calibration is to measure ττ . ττ is measured by connecting the transmitted LB4XXX
power sensor to the reflectometer; referred to as a thru.
The thru measurement is
= 1 = ττ (cL/aL),
ττ = (aL/cL).
L1 = 1 is the liner transmission gain for the thru;
ττ is the linear transmission tracking
cL is the linear measured transmitted square root of power for the thru;
is the linear measured forward square root of power for the thru.
Form of the solution in dB
Transmission gain or loss is
+ cdB - adB.
LdB is the dB gain or loss of the DUT;
the dB transmission tracking correction;
cdB is the dB measured transmitted power;
is the dB measured forward power.
The thru measurement is
L1dB = 1 =
+ cLdB - aLdB, or
= aLdB - cLdB.
L1dB = 0 is the dB transmission gain for the
is the dB transmission tracking correction term;
cLdB is the dB measured transmitted power for the
aLdB is the dB measured forward power for the thru.
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Posted October 19,