Reflection/Transmission Measurements Using a LadyBug PowerSensor+™

Obtaining
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.

October 2013

Application Note

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
Measurement Solution:

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:

Easy to integrate ATE software components.

Fast 2000 settled points/second enabling real time measurements

Wide -60 dBm to +20 dBm dynamic range

Signal separation device selection:

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.

Example 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:

As 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.

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.

Correction:

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.

Reflection Measurement
and Correction:

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
= τ
(b/a).

Where:

ρ
is the liner reflection coefficient of the DUT; 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
τ.

Reflection Calibration:

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 is

ρ_{O}
= |1| =
τ_{O}
(b_{O}/a_{O}), or τ_{O}
= (a_{O}/b_{O}).

Where:

ρ_{O}
= |1| is the liner magnitude reflection coefficient for an ideal
open; τ_{O} is
the liner tracking measurement for the open calibration; b_{O}
is the linear measured reflected square root of power for the open calibration;
a_{O} is the linear measured forward square root of power for
the open calibration.

Measurement of the short is

ρ_{S}
= |-1| =
τ_{S}
(b_{S}/a_{S}), or τ_{S}
= (a_{S}/b_{S}).

Where:

ρ_{S}
= |-1| is the liner magnitude reflection coefficient for an ideal
short; τ_{S}
is the liner tracking measurement for the short calibration; b_{S}
is the linear measured reflected square root of power for the short
calibration; a_{S} is the linear measured forward square
root of power for the short calibration.

Determine
τ
by averaging
τ_{O}
and τ_{S}

τ
= (τ_{O}
+ τ_{S})/2.

It should be noted the either
τ_{O}
or τ_{S}
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 =
ρ_{dB}
= τ_{dB}
+ b_{dB} - a_{dB}.

Where:

RL =
ρ_{dB}
is the return loss of the DUT; τ_{dB}
is the tracking correction in dB; b_{dB} is the reflected
power measurement in dBm; a_{dB} is the forward power measurement
in dBm.

ρ_{O}
= 0 is the return loss for an ideal open; τ_{O}
is the tracking measurement in dB for the open calibration; b_{O}
is the reflected power measurement in dBm for the open calibration;
a_{O} is the forward power measurement in dBm for the open calibration.

ρ_{S}
= 0 is the return loss for an ideal short; τ_{S} is
the tracking measurement in dB for the short calibration; b_{S}
is the reflected power measurement in dBm for the short calibration;
a_{S} is the forward power measurement in dBm for the short
calibration.

Determine
τ
by taking the linear average of
τ_{O}
and τ_{S}

τ
= 20 x Log10( 10^(-τ_{O}/20)
+ 10^(-τ_{S}/20))/2.

Transmission 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

Transmission gain or loss is

L =
τ_{τ}
(c/a).

Where:

L is the liner transmission gain or loss
of the DUT; τ_{τ} is
the linear transmission tracking correction; c is the linear measured
transmitted square root of power; a is the linear measured forward
square root of power.

Measurement of
τ_{τ}

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

L_{1} = 1 =
τ_{τ}
(c_{L}/a_{L}), or τ_{τ}
= (a_{L}/c_{L}).

Where:

L_{1}
= 1 is the liner transmission gain for the thru; τ_{τ}
is the linear transmission tracking correction term; c_{L}
is the linear measured transmitted square root of power for the thru;
a_{L} is the linear measured forward square root of power for
the thru.

Form of the solution in dB

Transmission
gain or loss is

L_{dB} =
τ_{τ}_{dB}
+ c_{dB} - a_{dB}.

Where:

L_{dB}
is the dB gain or loss of the DUT; τ_{τ}_{dB} is
the dB transmission tracking correction; c_{dB} is the dB
measured transmitted power; a_{dB} is the dB measured forward
power.

L_{1dB}
= 0 is the dB transmission gain for the thru; τ_{τ}_{dB}
is the dB transmission tracking correction term; c_{LdB}
is the dB measured transmitted power for the thru; a_{LdB}
is the dB measured forward power for the thru.

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