Balanced Amplifier IP3 & P1dB Improvement Due to 90° Hybrid Couplers
by Thomas Shafer
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(206) 920-5659  A balanced amplifier design is defined by two amplifiers of equal gain, 1dB compression point (P1dB) and Third-Order Intercept (IP3), arranged in the configuration shown to the right. The couplers are 3 dB hybrids, where the input power is split equally between a 0°and a 90° port. The unused ports are terminated in the system impedance typically 50 Ω. Reflections from the input and output ports of the amplifiers are shunted to the unused port of each coupler, giving the entire arrangement a matched impedance.
For a single, unbalanced amplifier, the output third-order intercept point is defined by the device specifications. The third-order intermodulation products (IM3) will appear at approximately 2Δ dB below the signal power of the primary tones at the device output where Δ = IP3in Pin = IP3out - Pout (in other words, 3Χ15 dB below the output-referred 3rd order intercept point).  Consider the example of an amplifier with the gain and linearity specs shown above. If the input power of the two primary tones at 1 and 2 are both -30 dBm, then at the output, third-order Intermodulation products (IM3s) will appear at 21 - 2 and 22 1, at a power of:
IM3out = Pout - 2(IP3out Pout) = (Pin + G) - 2(IP3out (Pin + G)) = (-30+24) (2(29 (-30+24))) = -6 2(29-(-6)) = -76 When this amplifier is used in the balanced configuration above, the primary tones are split equally (-3dB) at the outputs of the first hybrid, with one signal phase-shifted 0°, and the other phase-shifted 90°. After the two split signals are amplified to [Pin 3dB + G], they re-combined, with the phase-shift swapped, so that the recombined signal is equal to [Pin + G] Π90°. However, since the input signal to each amplifier has been decreased by 3dB, the IM3s at the output of each amplifier have been decreased by 9dB. Specifically, IM3out = Pout - 2(IP3out Pout) = ((Pin 3dB) + G) - 2(IP3out ((Pin 3dB) + G))) = ([-30dBm 3dB]+24dB) (2(29dBm ([-30dBm 3dB]+24dB))) = -9dBm 2(29dBm (-9dB)) = -85dBm The IM3s are combined in-phase through the output 3dB hybrid (remember the 90° phase shift is swapped), which is effectively adding 3dB to the number above. Thus the IM3s of the balanced amplifier are -82dBm, which is 6dB lower than the single amplifier. The effective IP3out can be calculated with the formula IP3out (dBm) = Pout (dBm) +0.5[Pout (dBm) IM3out(dBm)] = (Pin + G) + 0.5[(Pin + G) IM3out] = (-30dBm + 24dB)+0.5[(-30dBm + 24dBm) (-82dBm)] = +32dBm 3dB higher than the single amplifier QED
Here is a slightly different approach that springboards off of Thomas' work, but does not concern itself with the phases of the signals through the splitter and combiner. This solution is also valid using standard 2-way splitters/combiners with individual matched amplifiers that exhibit excellent input and output VSWR. --- Kirt Blattenberger Assume individual device parameters are the same as in Thomas' example, and that Pin for each of the two system input signals is -30 dBm at the system input. The 3 dB coupler splits the signals equally, so at the amplifier inputs the signals are -33 dBm. 3rd-order products at the output of each device are: IM3out = Pout - 2(IP3out Pout) = 3Pout - 2IP3 = 3(-33dBm +24dB) 2(29dBm) = -27dBm - 58dBm = -85dBm The IM3out after combining both amplifiers is -85dBm + 3dB = -82dBm Now, since the gain of the balanced amplifier is the same as the individual devices, we have: Gain = 24dB IM3out = -82dBm Pout = -30dBm + 24dB = -6dBm Cranking those numbers back into the IP3 formula yields: IP3 = 1/2 (3Pout - IM3out) = 1/2 (3-6 - -82) = 32dBm QED (again) Note: By a similar analysis, it can be shown that the 1 dB compression point (P1dB) also
improves by 3 dB. Read about the characteristics of a 3 dB hybrid coupler that make it a great tool for building amplifiers
whose individual devices do not match the system impedance, but do match each other's impedance. |