Power combining theoretically increases an amplifier's effective output power by coherently summing N identical output stages. For example, if one output stage produces 1 W power, coherently combining four stages will effectively increase the output power to 4 W. Practically, the output power will be degraded by the combiner loss and the practical amplitude and phase errors introduced. As the number, N, of channels increases, the difficulty in maintaining minimally acceptable phase and amplitude errors while minimizing the summing device losses grows substantially. In this article, power-combining techniques will be analyzed for two devices, but these approaches can easily be extrapolated to higher-order combining systems.

Image phase mixing is a technique of frequency converting an upper or lower sideband to an intermediate frequency (IF). This manipulation is accomplished by splitting an RF signal into two channels and mixing each of the channels with a local-oscillator (LO) signal. The two IF signals are combined in an unterminated quadrature coupler, with one output yielding the upper sideband and other output producing the lower sideband.

Power combining and image-rejection techniques using an image phase mixer are the respective vector addition and subtraction of two signals. Doubling the output power capability of an amplifier is typically accomplished by dividing the signal into two paths, amplifying the signal with two identical power amplifiers and summing the resulting signals together. The gain is not affected but the output power, i.e., the 1-dB compression point and respective third-order intercept point, is increased by 3 dB.

In real systems, dividers, amplifiers, and combiners are not ideal and have respective gain (amplitude) and phase errors. The effects of the gain and phase errors are readily understood if the signals are represented as phasors (for example, Asinθ , where A is the magnitude in V and is the phase in deg.). The input is a voltage vector divided into two paths, amplified and recombined. Any error in the components shows up as changes in the magnitude and phase. Ideally, the amplitudes are identical and the vectors are in phase, doubling the value of the individual vectors and effectively doubling the output capability of the individual amplifiers. Amplitude and phase errors due to the mismatch of the components degrade the output because the magnitude of the sum vector at an offset angle is less than that of an in-phase vector.

The actual output power capability of this real device can be determined by laying the larger vector (B) on the abscissa and breaking the other vector (A) into its quadrature components (Asinq and Acosq). Summing the two vectors produces two quadrature components, Asinq and B + Acosq. The magnitude of the vector sum is the square root of the sum of the squares of each of the quadrature components.

Multiplying the individual terms yields:

Simplifying the results gives:

If B is the normalized vector, B = 1, the magnitude of the voltage vector with respect to the ideal system will be:

The output power can be represented as the square of the voltage:

A² is the equivalent power of the A vector:

Substituting PA for A2 and factoring out 2(1+PA) yields:

In a perfect system, vector A is equal to vector B and P_A = 1 and P_out = 4. Therefore, the normalized output power, i.e. with respect to the initial input signal is P_nor:

Parameter P_nor in dB [P_nor(dB)] is the normalized loss due to amplitude and phase mismatches:

where the loss due to unequal signals is P_sig(dB):

and the added loss due to amplitude and phase mismatch is ΔP(dB):

These equations break power-combining errors into two categories leading to three power combining error curves:

1. The total power for two unequal signals (zero phase error).
2. The loss due to phase and amplitude mismatch with respect to the sum of two unequal signals in phase (Fig. 1) .
3. The total power loss due to unequal signals and phase mismatches with respect to two equal signals that are in phase at the maximum output power level (Fig. 2 and Fig. 3) .

In power combining, the signal of interest is split into two equal paths, amplified, and combined. If one channel has more loss than the other, the total output power will be lower than expected, where Psig(dB) is the loss with respect to two signals at the maximum power level: