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# Explanation of PA for quasi-constant amplitude carrier

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#### Humungus

##### Full Member level 6
Could somebody explain why the PA for quasi-constant amplitude carriers does not need to be highly linear?

For instance, some systems using OQPSK (quasi-cosntant evelope) have a simple PA. So, why do we pass the I and Q signal through rised cosine filters if, after all, the PA will introduce spurs?

constant envelope signal enable us to use high efficient power amplifier without distortion. raise cosine filter is used to bandlimit the baseband signal, so that they fall into the specific band and have very low out of band emission

The PA should be linear for two reasons:
1. To prevent power spill to adjacent channels (out-of-band mixing)
2. To prevent distortion inside your own channel (in-band mixing)

For some modulation types (e.g. FM), reason (2) does not exist, and hence the reduced linearity requirement. Reason (1) is why you do spectral shaping, because illinearity is equivalent to a convolution in the frequency domain, so the more tapered the spectrum, the less spill to adjacent frequency bands

for a constant envelope signal, the amplifier will not need to be linear. even a highly nonlinear amplifier can be use to amplify a FM/PM signal. multiplication in time domain means convolution in frequency domain and vice versa.

quasi-constant amplitude carrier has a very low (almost zero dB) peak-to-average ratio. Which means that the signal does not have peaks (its peak is equal to its average), like FM signals as said above, or GSM signal.

Signals with high peaks (like CDMA signals) will clip at their peaks, because the amplifier saturates at high peaks.

Having no high peaks means that the amplifier can be driven harder, without worrying about peak clipping.

Those an amplifier with constant amplitude is more efficient, since you do not need to back-off the average power to avoid peak clipping.

Peak clipping will result spectral-regrowth (as said above).

Hope this helped.

Cheers...

Humungus, this is very good question. All my text-books say that a constant amplitude
allows the use of a C-class PA. But they all lack the formal explanation.

Is it only because of the need of lower back-off to avoid peak clipping?
But a C-Class amplifier is operated way beyond the linear region. It is already clipping.

What if we go through the math and actually look at a nonlinear amplifier?
You could represent the PA with a series, for example y(t)=c1*x(t)+c2*x(t)^2+c3*x(t)^3....

I think you GENERALLY have much more spectral components coming out if the amplitude of your incoming signal-amplitude
also variies: x(t)=[A*cos(w1*t)]*cos(w2*t)

Regards

I have some experience in analog BB, but I'm a newbie (??) in RF.

Thanks and regards to all

Humungus

>Is it only because of the need of lower back-off to avoid peak clipping?
But a C-Class amplifier is operated way beyond the linear region. It is already clipping.

the drain of a Class C amplifier conducts less than half a sinuisodal period, thus, most of the time, the transistor is switch off, thus saving energy.

>What if we go through the math and actually look at a nonlinear amplifier?
You could represent the PA with a series, for example y(t)=c1*x(t)+c2*x(t)^2+c3*x(t)^3....

yes, the output of a class c amplifier creates lots of IMP and harmonics, that's why there is a resonator/filter at the output of class c amplifier. the final output will be a clean amplified x(t)

>I think you GENERALLY have much more spectral components coming out if the amplitude of your incoming signal-amplitude
also variies: x(t)=[A*cos(w1*t)]*cos(w2*t)

the expression give above consist of amplitude modulation, a constant amplitude signal has the expression like this:
x(t)=cos(w1*t+ s(t))
s(t) represent the phase function. the bandwidth of x(t) is determine by d/dt(s(t)). for FM, s(t) is a linear function.

as for reference, search for amplifier linearisation.

The raised cosine filters are needed to limit the bandwidth of the signal. Otherwise, it would take infinite RF bandwidth to reproduce the signal. You can easily see this on any simulation software. Now that you have amplitude information, you need an amplifier with lower amplitude distortion so that this informationis not corrupted. The closer the constellation passes through the origin, the more linearity is needed since the amplitude information is becoming greater and greater. The OQPSK requires less linearity than a QPSK since the constellation trajectory does not pass as close to the origin.

harkonnen said:
Is it only because of the need of lower back-off to avoid peak clipping?
But a C-Class amplifier is operated way beyond the linear region. It is already clipping.

True, class C is already clipping the valleys (minimums) of the signal, and this DOES introduce spectral re-growth. You can send AM signal through a class C amplifier, but it will be distorted. Broadcasting stations used class C for AM, but the distortion is tolerable by listeners. Other services (like cellular) cannot tolerate such a distortion.

Nobody uses a class C amplifier (even for constant amplitude cellular like GSM) these days. Everybody uses class AB. It also clips the minimums, but not as much as class C, and has more efficiency than class A.

Broadcast stations that use a class C final amplifier are not using it as a linear amplifier of a low level AM signal. They are applying the modulation to the class C stage itself. In this case, the (non) linearity of the class C amplifier does not distort the signal at all since it is just amplifying the constant envelope low level RF signal, not the AM modulated signal.

more details

To amplify (no pun intended) upon the previous post, the final amplifier tube power supply voltage is raised and lowered in acordance with the modulating voltage. In the old days this was done by putting a transformer in series with the B+ (High voltage to the plate) as it was called. The primary went to the plates of a push-pull power amplifier. In more modern times, the voltage to the final transistor amplifier is raised and lowered by using pulse width modulaltion in switching the B+ or Vcc on and off and low pass filtering it.

In all cases it is usual to detect the output signal and feed this back to the audio amplifier.

the method describe by flatulent is one of the linearisation technique call envelope elimination and restoration(EE&R). there are many linearisation available to tackle amplifier linearity issue, such as predistotion, feedforward, LINC, CALLUM and EE&R.

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