I’ve heard for the last 10 years or so that polar modulation will give spectrally-efficient modulation formats (OFDM, CDMA, etc.) the PA efficiency that they so lack nowadays.

I agree: polar modulation will give a boost in efficiency—when several problems are solved. Here are the challenges that plague polar modulation


Polar modulation takes band-limited I & Q signals and composes an amplitude signal a=sqrt(I^2 + Q^2) and a phase signal p = atan(Q/I). These are heavily non-linear functions. As a result, the resulting bandwidth of a and p are much larger than I/Q.

In addition, band-limiting a & p can have deleterious effects on the resulting RF signal. In order to maintain spectral masks (contain the near-in spectrum), multiples of the desired bandwidth need to be preserved in a and p.

We are essentially taking band-limited signals and decomposing them into wide-band signals (so that we can amplify them efficiently) to then recompose them into a final band-limited signal (I+jQ = a*exp(j*p))

A not-so good example of this bandwidth effect is the case where I=cos(wm*t) & Q=0. Then, the a=|cos(wm*t)| and ph = pi*sgn[cos(wm*t)]:

Discontinuity in phase and discontinuity in derivative of amplitude

However, this is not such a good example, since in some cases, this discontinuity in amplitude and phase can be reduced by allowing the amplitude to be positive and negative (i.e. a double-balanced mixer) and transferring the phase reversal from p to a:

Discontinuities in phase and amplitude cancel each other (when we allow a(t) to be positive or negative)

Unfortunately, this cannot be done with a transformer-coupled class-D configuration:


Another problem that plagues power modulators is signal leakage. Normally, the input to a power amplifier (PA) is a replica of its output, only lower in power. If this input then leaks to the output of the PA, no harm is done with respect to spectral masks:

Leakage of linear amplifier does not affect spectral mask

Polar modulators, however, have two inputs: amplitude a and phase p—neither of which look anything like the desired output.

The amplitude path is generally off-frequency (not with the RF carrier). However, the phase path p is modulated with the RF carrier and can leak through to the output. Note that this is a wide-band signal that will screw up the spectral mask:

Wideband modulated phase signal leaking to output disrupts output spectrum

In effect, this means that the dynamic range of the PA is limited by leakage of the phase signal. Note that this can greatly hinder power control—which I consider to be the true challenge of supply modulation.