Effects of Non-Ideal Reflection Coefficients on Delivered Power
- Updated2024-08-02
- 4 minute(s) read
Effects of Non-Ideal Reflection Coefficients on Delivered Power
The PXIe-5611 I/Q Modulator front panel connectors are designed to work in a 50 Ω environment. However, the connector impedances are not ideal because they are not exactly equal to 50 Ω. Deviation from ideal impedance can be evaluated as the reflection coefficient (Γ). Refer to the specifications document for your device for more information about voltage standing wave ratio (VSWR).
Reflection coefficient can be derived from VSWR with the following formula:
During characterization of the PXIe-5611 RF OUT and LO OUT front panel connectors for power accuracy calibration, the measurement device, a power meter, is connected to the RF OUT and LO OUT front panel connectors through an attenuator to improve the measurement device's reflection coefficient. Subsequently, the measurement device will look like an almost ideal (50 Ω) load. The output power level accuracy numbers in the specifications document for your device mention the accuracy under these conditions, while taking into account any deviations of the measurement device's impedance as seen by the PXIe-5611 RF OUT or LO OUT front panel connectors from an ideal 50 Ω.
When an external load is connected to either the PXIe-5611 RF OUT or LO OUT front panel connector, the accuracy of the power delivered to the external load depends on the external load's LO OUT and RF OUT reflection coefficient(ΓS can represent either the LO OUT or RF OUT reflection coefficient). ΓL and ΓS assume a reference of 50 Ω. The delivered power to the external load is bounded by the following equation:
where Pdel represents the delivered power, in mW
Pexpected represents the expected power passed out of the front panel connectors, in mW
ΓL represents the load or device under test connected to the PXIe-5611
ΓS represents the RF OUT or LO OUT reflection coefficient
accuracy power represents output power level accuracy for the power and temperature range you are returning, in dB, according to your device specifications.
If Pexpected is given in dBm, then the formula 
converts dBm power into mW power. ΓL and ΓS are in non-dB and linear format, where 50 Ω results in Γ = 0 and |Γ| = 1 for a short or an open. Use the formula 10Log10(Pdel) to convert the delivered power to the load from mW to dBm. The output power level accuracy specification is what your device specifications identifies as the power accuracy for the power and temperature range you are trying to return. Computing the delivered power depends on the sign of the reflection coefficients. Compute the delivered power to the external load twice with the following denominators and account for the different results in your error budget:
and
Example
Assume that at the carrier frequency and power level, you want to generate a signal at the PXIe-5611 RF OUT front panel connector. The PXIe-5611 RF OUT front panel connector has a reflection coefficient equal to –16 dB. As a result, |ΓS| equals 0.1585. Assume also that the PXIe-5611 RF OUT front panel connector connects to a load where the reflection coefficient at the same desired frequency is –14 dB. As a result, |ΓS| equals 0.1995. If the accuracy specification for the PXIe-5673/5673E Vector Signal Generator is 0.5 dB at the generated frequency and power level, then two possible bounds for the delivered power are represented in the following equations:
Adding an in-line external attenuator (a pad) at the PXIe-5611 RF OUT and LO OUT front panel connectors improves the reflection coefficient by double the attenuation amount in dB. For example, connecting a 3 dB pad at the PXIe-5611 RF OUT front panel connector reduces the output power by 3 dB (approximately half of the power) and reduces the magnitude of the reflection coefficient by 6 dB (approximately half of the magnitude).
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Note In the preceding example, and |Γ'S| = 0.07943. |