By adding a third LBXXA Power Sensor transmission measurements (S21 or S12) can be made. Port match of the power sensor and of the reflectomer 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 .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

ρO = |1| = τO (bO/aO), or

τO = (aO/bO).

Where:

ρO = |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.

Measurement of the short is

ρS = |-1| = τS (bS/aS), or

τS = (aS/bS).

Where:

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 calibration;

aS is the linear measured forward square root of power for the short calibration.

Determine τ by averaging τO and τS

τ = (τO + τS)/2.

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 .44 dB (0.12 dB X 2 + 0.1 dB X2).

Form of the solution in dB.

#### Return Loss is:

RL = ρdB = τdB + bdB – adB.

Where:

RL = ρdB is the return loss of the DUT;

τdB is the tracking correction in dB;

bdB is the reflected power measurement in dBm;

adB is the forward power measurement in dBm.

**Reflection Tracking Calibration:**

Measurement of the open in dB is

RLO = ρdBO = τdBO + bdBO – adBO, or

τdBO = adBO – bdBO.

Where:

ρO = 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, or

τdBS = adBS – bdBS.

Where:

ρS = 0 is the return loss for an ideal short;

τS is 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 τS

τ = 20 X LOG10( 10^(-τO/20) + 10^(-τS/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 = ττ (c/a).

Where:

L is the liner transmission gain or loss of the DUT;

ττ 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 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

L1 = 1 = ττ (cL/aL), or

ττ = (aL/cL).

Where:

L1 = 1 is the liner transmission gain for the thru;

ττ is the linear transmission tracking correction term;

cL is the linear measured transmitted square root of power for the thru;

aL is the linear measured forward square root of power for the thru.

Form of the solution in dB

Transmission gain or loss is

LdB = ττdB + cdB – adB.

Where:

LdB is the dB gain or loss of the DUT;

ττdB is the dB transmission tracking correction;

cdB is the dB measured transmitted power;

adB is the dB measured forward power.

Measurement of ττdB

The thru measurement is

L1dB = 1 = ττdB + cLdB – aLdB, or

ττdB = aLdB – cLdB.

Where:

L1dB = 0 is the dB transmission gain for the thru;

ττdB is the dB transmission tracking correction term;

cLdB is the dB measured transmitted power for the thru;

aLdB is the dB measured forward power for the thru.