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The trial frequency bands … Expand. Highly Influenced. View 11 excerpts, cites methods. A fully integrated Doherty-amplifier for 5. View 2 excerpts, cites background. The increasing demand for higher data rates in wireless communication such as IEEE View 4 excerpts, cites methods and background.

To achieve a wide tuning range, … Expand. View 5 excerpts, cites background and methods. Direct-conversion radio transceivers for digital communications.

Direct-conversion is an alternative wireless receiver architecture to the well-established superheterodyne, particularly for highly integrated, low-power terminals.

Its fundamental advantage is that … Expand. Fully integrated CMOS oscillators are of great interest for use in single-chip wireless transceivers. In most oscillator circuits reported to date that operate in the 0. A wide variety of voltage mixers and samplers are implemented with similar circuits employing switches, resistors, and capacitors.

Of course we would fix it up so that a battery would not be needed to supply the bias voltage. The linear RF power amplifier would be the major part of this transmitter.

Let us find the efficiency for the transmitter of Figure 6. Note that the maximum output voltage is Vdc, the power supply voltage.

Refer to the amplifier circuit of Figures 3. These amplifiers are not linear in the normal sense, that is, the output signal amplitude is not a constant multiple of the input signal amplitude. But, for a fixed input RF amplitude, the output amplitude is proportional to the supply voltage. These amplifiers can therefore be used as high-power multipliers that form the product of the power supply voltage times a unit sine wave at the RF frequency.

Furthermore, the efficiency of these amplifiers, which is high, is essentially independent of the supply voltage. These amplifiers are discussed in detail in Chapter 9. Let us look at the overall efficiency of transmitters using these amplifiers. As explained above, a class-C RF amplifier acts as a high-power multiplier. In the traditional tube-type circuit of Figure 6. Audio voltage produced by the modulator appears across the secondary winding and adds to the bias voltage.

With no audio present, the class-B audio amplifier consumes negligible power and the bias voltage supply provides power for the carrier. A 50 watt transmitter thus requires a modulator that can supply 25 W of audio power. Again, this result is for a single tone, but is essentially the same for speech or music.

Class-B platemodulated AM transmitter. Class-C RF amp. Audio drive From dc supplies 64 Radio-frequency electronics: Circuits and applications Let us find the efficiency of this transmitter.

To find the efficiency of the class-B modulator, we must know not only its peak output voltage, but also the mean of the absolute value of its output voltage. Note that this last piece of information was not needed in the analysis of the class-B RF amplifier transmitter discussed above. Let us just assume the modulating signal is a single audio sine wave whose power is 0.

With that assumption, the modulator will have an efficiency of 0. Optical fiber There are several newer methods to produce AM with even higher efficiency.

All use switching techniques. The modulator shown in Figure 6. It uses solid-state switches to add the voltage of many separate low-voltage power supplies, rather than tubes or transistors to resistively drop the voltage of a single high-voltage supply. The modulator of Figure 6.

Audio drive pulse width modulation Class-C final RF amp. Like the class-C amplifier, the amplitude of their output sine wave is proportional to the dc supply voltage. These superpower transmitters use vacuum tubes.

Standard AM broadcast band transmitters in the U. For this power and lower powers, new AM transmitters manufactured in the U. These transmitters combine power from a number of modular amplifiers in the 1 kW range. Most FM transmitters over about 10 kW still use vacuum tubes, but solid-state FM transmitters are available up to about 40 kW. Stereophonic sound was added to FM broadcasting around Thus the system is backwardly compatible, just as color television was compatible with existing black and white television receivers.

The demodulator to recover the L-R signal is discussed in Chapter Stereo was added to AM radio broadcasting around Several systems competed to become the standard, but the public was largely indifferent, having already opted for FM stereo. Compatible digital broadcasting has recently been introduced, with versions for both the AM and FM bands.

The digital signal, which can be produced by a separate transmitter and may even use a separate antenna, uses COFDM Coded Orthogonal Frequency-Division Multiplexing , a modulation system, described in Chapter This system is intended to be a stepping-stone to all-digital radio broadcasting in the traditional AM and FM bands.

IBOC broadcasting equipment is equipped to transmit an all-digital mode, to be used if and when the traditional analog broadcasting is discontinued. Problems Problem 6. What is the ratio of sideband power to carrier power? Problem 6. Suppose you are trying to listen to a distant AM station, but another station on the same frequency is coming in at about the same strength. Will you hear both programs clearly?

If not, how will they interfere with each other? During periods where the audio signal level is low, the amplitude of an AM signal varies only slightly from the carrier level. The modulation envelope, which carries all the information, rides on top of the high-power carrier.

If the average amplitude could be decreased without decreasing the amplitude of the modulation, power could be saved. Discuss how this might be accomplished at the transmitter and what consequences, if any, it might have at the receiver. Show how a PM transmitter can be used to generate FM. Consider an FM transmitter modulated by a single audio tone. As the modulation level is increased, the spectral line at the carrier frequency decreases. Find the value of the modulation index that makes the carrier disappear completely.

Draw block diagrams of a transmitter and receiver for this system. CHAPTER 7 Radio receivers In this chapter we will be mostly concerned with the sections of the receiver that come before the detector, sections that are common to nearly all receivers: AM, FM, television, cell phones, etc.

Basic specifications for any kind of radio receiver are gain, dynamic range, sensitivity and selectivity, i. Sensitivity is determined by the noise power contributed by the receiver itself. Usually this is specified as an equivalent noise power at the antenna terminals. One milliwatt of audio power into a typical earphone produces a sound level some dB above the threshold of hearing.

Let us specify that a receiver, for comfortable earphone listening, must provide 50 dB more than this threshold of hearing, or 10—8 watts. You can see that, with efficient circuitry, the batteries in a portable receiver could last a very long time!

Sound power levels are surprisingly small; you radiate only about 1 mW of acoustic power when shouting and about 1 nW when whispering. How much signal power arrives at a receiver? A crystal diode rectifier recovered the modulation envelope, converting enough of the incoming RF power into audio power to drive the earphone.

A simple LC tuned circuit served as a bandpass filter to select the desired station and could also serve as an antenna matching network. The basic crystal set receiver is shown in Figure 7. Figure 7. Self-powered crystal set receiver. Antenna Tuner Diode Headphones The considerations given above show that a self-powered receiver can have considerable range.

But when the long-wire antenna is replaced by a compact but very inefficient loop antenna and the earphone is replaced by a loudspeaker, amplification is needed.

In addition, we will see later that the diode detector, when operated at low signal levels, has a square-law characteristic, which causes the audio to be distorted. For proper envelope detection of an AM signal, the signal applied to a diode detector must have a high level, several milliwatts. The invention of the vacuum tube, followed by the transistor, provided the needed amplification. Receivers normally contain both RF and audio amplifiers. RF amplification provides enough power for proper detector operation, while subsequent audio amplification provides the power to operate loudspeakers.

TRF receiver. RF amp — kHz RF amp Detector Audio amp Spkr required the user to adjust several dials often with the aid of a tuning chart or graph.

Note that all the inductors and capacitors should be variable in order to tune the center frequency of the bandpass filters and also maintain the proper bandwidth, which is about 10 kHz for AM.

In a practical circuit, the bandpass filters would use a coupled-resonator design rather than the straightforward lowpass-to-bandpass conversion design shown here.

Most of these adjustments were eliminated with the invention of the superheterodyne circuit by Edwin H. Armstrong in This frequency is known as the intermediate frequency or IF. The superheterodyne is still the circuit used in nearly every radio, television, and radar receiver. Among the few exceptions are some toy walkie-talkies, garage-door openers, microwave receivers used in radarcontrolled business place door openers, and highway speed trap radar detectors. The AM detector here is still a diode, i.

In Chapter 18 we will analyze this detector, among others. All the RF gain can be contained in the fixed-tuned IF amplifier, although we will see later that there are sometimes reasons for having some amplification ahead of the mixer as well.

Note: There was indeed a heterodyne receiver that preceded the superheterodyne. Detector Audio amp. Speaker kHz center freq. Standard superheterodyne receiver for the AM broadcast band. With respect to signals at the input to the mixer, the receiver will simultaneously detect signals at the desired frequency and also any signals present at an undesired frequency known as the image frequency.

All the mixers we have considered will also produce a kHz IF signal from any input signal present at kHz, i. If the receiver has no RF filtering before the mixer and if there happens to be a signal at kHz, it will be detected along with the desired kHz signal.

A bandpass filter ahead of the mixer is needed to pass the desired frequency and greatly suppress signals at the image frequency. In this example, the tracking requirement is not difficult to satisfy; since the image frequency is more than an octave above the desired frequency, the simple one-section filter shown in Figure 7. Note, though, that 20 dB is not adequate if a signal at the image frequency is 20 dB stronger than the signal at the desired frequency.

What if a receiver with the same kHz IF frequency is also to cover the short-wave bands? As explained above, the center frequency of the filter must be track with a kHz offset 71 Radio receivers from the L. Image rejection is not simple when the IF frequency is much lower than the input frequency. Solving the image problem A much higher IF frequency can solve the image problem.

The image frequency would be As the radio is tuned up to the top end of the AM broadcast band, kHz, the image frequency increases to In this case, a fixed-tuned bandpass filter, wide enough to cover the entire broadcast band, can be placed ahead of the receiver to render the receiver insensitive to images. This system is shown in Figure 7.

Only the local oscillator needs to be changed to tune this receiver. Image-free broadcast receiver using a 10 MHz IF. IF amp. Speaker 10 MHz center freq. If the input band is wider, e. Even at 10 MHz, a bandwidth of 10 kHz implies a very narrow fractional bandwidth, 0.

A solution to both the image problem and the narrow fractional bandwidth problem is provided by the double-conversion superhet.

Double conversion superhet Figure 7. The MHz first IF filter can be wider than the ultimate passband. Suppose, for example, that the first IF section has a bandwidth of kHz.

The second L. IF bandpass filter 10 MHz center freq. Double conversion superhet. Speaker kHz center frequency 10 kHz bandwidth 2nd local osc. This system has its own special disadvantages: the receiver usually cannot be used to receive signals in the vicinity of its first IF, since it is difficult to avoid direct feedthrough into the IF amplifier.

The front-end image filter is usually a 30 MHz lowpass filter. In as much as modern crystal filters can have a fairly small bandwidth even at 40 MHz, the output of the first IF section can be mixed down to a second IF with a much lower frequency. Sometimes triple conversion is necessary when the final IF frequency is very low, e. The use of first IF frequencies in the VHF region requires very stable local oscillators but crystal oscillators and frequency synthesizers provide the necessary stability.

Oscillator phase noise was a problem in the first generation of receivers with synthesized local oscillators; the oscillator sideband noise was shifted into the passband by strong signals near the desired signal but outside the nominal passband. Image rejection mixer Another method of solving the image problem is to use an image rejection mixer, such as the circuit shown in Figure 7.

This circuit uses two ordinary mixers multipliers. Image rejection mixer. Thus, this mixer rejects signals above the L. The same circuit crops up in Chapter 8, as a single-sideband generator. In practice this circuit might provide 20—40 dB of image rejection. It can be used together with the standard filtering techniques to get further rejection. Zero IF frequency — direct conversion receivers The evolution of the superhet, which was always toward higher IF frequencies and multiple conversions, has taken a new twist with the advent of the nearly limitless signal processing power available from DSP chips.

To see this, note that the original signal could be easily reconstructed from the I and Q signals. Lowpass filtering of the I and Q signals determines the passband of the receiver, e. The classic image problem, severe at low IF frequencies, disappears when the IF frequency is zero. The low-frequency I and Q signals can be digitized directly for subsequent digital processing and demodulation see Problem 7.

No bulky IF bandpass filters are required. Everything on this diagram plus an L. Direct conversion receiver. The output sound level of an FM receiver, depending on the design of the demodulator, may not vary with signal level but overloading the IF amplifier stages will still produce distortion, so FM receivers also need AGC.

Any AGC circuit is a feedback control system. In simple AM receivers the diode detector provides a convenient dc output voltage that can control the bias current and hence gain of the RF amplifiers. The controlled bias current can also be used to drive a signal strength indicator.

Here the interfering pulses are of such short duration that the IF stages can be gated off briefly while the interference is present. The duty cycle of the receiver remains high and the glitch is all but inaudible or invisible.

An important consideration is that the gating must be done before the bandwidth is made very narrow since narrow filters elongate pulses. Any desired filter amplitude and phase response can be realized. Besides direct-conversion receivers on a chip, there are many singlechip superhet chips, usually using image cancelling mixers followed by digital bandpass filters operating at low IF frequencies.

Adaptive digital filters can correct for propagation problems such as multipath signals. Digital modulation techniques are discussed in Chapter Problems Problem 7. The FM broadcast band extends from 88 to MHz. Standard FM receivers use an IF frequency of What is the required tuning range of the local oscillator? Problem 7. Why are airplane passengers asked not to use radio receivers while in flight? Two sinusoidal signals that are different in frequency, if simply added together, will appear to be a signal at a single frequency but amplitude modulated.

When they are still at slightly different frequencies, the sound seems to pulsate slowly at a rate equal to their frequency difference. Using an AM receiver in an environment crowded with many stations, you will sometimes hear an annoying high-pitched 10 kHz tone together with the desired audio. If you rock the tuning back and forth the pitch of this tone does not change. What causes this? Can it be blamed on the receiver? Answer: Yes. Using modern components and digital control, we could build good TRF radios.

What advantages would such a radio have over a superheterodyne? What disadvantages? You may have observed someone listening to distorted sound from an AM radio whose tuning is not centered on the station. What is going on here? Why would a radio not have sufficient bandwidth and why would insufficient bandwidth cause some listeners to tune slightly off station?

Design a direct-conversion AM broadcast receiver using digital processing of the I and Q signals. Assume that the L. Hint: compute the input signal amplitude from the digitized I and Q signals. Then feed this stream of amplitudes into a D-to-A converter. Almost five pounds of practical circuits, explanations, and construction information. Good concise discussion of receivers. A whole course in itself. The third edition includes material on digital processing in receivers.

But viewed in the frequency domain, as in Chapter 6, this system shows some obvious inefficiencies. Since its amplitude and frequency are constant, it carries virtually no information. The information is in the sidebands.

Second, the upper and lower sidebands are mirror images of each other, so they contain the same information. Could they not suppress filter away one sideband, making room for twice as many stations on the AM band? The answer to both questions is yes but, in both cases, the simple AM receiver, with its envelope detector, will no longer work properly. Economics favored the simplicity of the traditional AM receiver until it because possible to put all the receiver signal processing on an integrated-circuit chip, where the additional complexity can have negligible cost.

In this chapter we examine alternate AM systems that remove the carrier and then at AM systems that reduce the signal bandwidth or double the information carried in the original bandwidth. It is easy enough to modify the transmitter to eliminate the carrier. Review the circuit diagram given previously for an AM transmitter Figure 6. If we replace the bias battery by a zero-volt battery a wire , the carrier disappears. To restore the missing carrier we might try the receiver circuit shown in Figure 8.

The locally generated carrier, from a beat frequency oscillator BFO , is simply added back into the IF signal, just ahead 77 78 Radio-frequency electronics: Circuits and applications Figure 8. The energy saved by suppressing the carrier can increase battery lifetime in walkie-talkies by a factor of maybe The modulation schemes used in many cell phones after the first generation likewise do away with battery-draining constant carriers.

In a superheterodyne receiver, we only have to generate this carrier at one frequency, the intermediate frequency IF. As you would expect, the added carrier must have the right frequency. But it must also have the right phase. Suppose, for example, that the modulation is a single audio tone at Hz. These example waveforms are shown in Figure 8. In the model transmitter of Figure 6. In principle, the receiver could have a tuned IF amplifier with a narrowband gain peak at the center frequency to bring the pilot carrier up to full level.

The sidebands are mirror images of each other so they carry the same information and one will do. We will discuss later three methods to eliminate one of the sidebands from a DSBSC signal, but the first and most obvious method is to use a bandpass filter to select the desired sideband. Take the previous example of a single Hz audio tone. The SSB transmitter will put out a single frequency, Hz above the frequency of the suppressed carrier if we have selected the upper sideband.

This signal will appear in the receiver Hz away from the IF center frequency. Suppose we are still using the BFO and envelope detector. Detection of DSSC by adding a local carrier.

So far, so good. But suppose the signal had been two tones, one at Hz and one at Hz. Unwanted signals are produced by the IF components beating with each other; their strength is proportional to the product of the two IF signals.

The strength of each wanted component, on the other hand, is proportional to the product of its amplitude times the amplitude of the BFO. In the receiver shown in Figure 8. The output of this detector is, by the distributive law of multiplication, the sum of the products of each IF signal component times the BFO signal.

There are no cross-products of the various IF signal components. While a product detector does not produce cross-products intermodulation distortion of the IF signal components, the injected carrier should ideally have the correct phase. The wrong phase is of no consequence in our single-tone example. But when the signal has many components, their relative phases are important. A waveform will become distorted if all its spectral components are given an identical phase shift see Problem 8.

It is only when every component is given a phase shift proportional to its frequency that a waveform is not distorted but only delayed in time. Therefore a single-sideband transmitter, like the double-sideband transmitter, should really transmit a pilot carrier and the receiver should lock its BFO phase to this pilot.

Some SSB systems do just that. But for voice communications it is common to use no pilot. Speech remains intelligible and almost natural-sounding even when the BFO phase is Figure 8.

SSBSC receiver using a product detector. When the frequency is too high, a demodulated upper sideband USB voice signal has a lower than natural pitch. When it is too low, the pitch is higher than natural.

If the BFO phase happens to be correct, the output will have maximum amplitude. For an intermediate-phase error the amplitude will be reduced. Advantages of SSB Single-sideband, besides not wasting power on a carrier, uses only half the bandwidth, so a given band can hold twice as many channels. Halving the receiver bandwidth also halves the background noise so there is a 3-dB improvement over conventional AM in signal-to-noise ratio.

When a spectrum is crowded with conventional AM signals, their carriers produce annoying beat notes in a receiver a carrier anywhere within the receiver passband appears to be a sideband belonging to the spectrum of the desired signal.

With single-sideband transmitters there are no carriers and no beat notes. Radio amateurs, the military, and aircraft flying over oceans use SSB for short-wave 1. In the filter method of Figure 8. This filter usually uses crystal or other high-Q mechanical resonators and has many sections. It is never tunable, so the SSB signal is generated at a single frequency a transmitter IF frequency and then mixed up or down to the desired frequency.

The filter, in as much as it does not have infinitely steep skirts, will cut off some of the low-frequency end of the voice channel. The audio phase-shift network is usually implemented with two networks, one ahead of each mixer.

The second term also 1 Human perception of speech and even music seems to be remarkably independent of phase. When an adjustable allpass filter is used to produce arbitrary phase vs. SSB generator — filter method. Figure 8. SSB Generator — phasing method. If the adder is changed to a subtractor by inverting the polarity of one input , the output will be the upper rather than the lower sideband. A third method [2] needs neither a sharp bandpass filter nor phase-shift networks.

SSB generator — Weaver method. The second set of mixers then works the same way as the two mixers in the phasing method. Referring to Figure 8. Linear amplifiers then produce the required power for the antenna.

There is, however, a way to use a class-C or class-D amplifier with simultaneous phase modulation and amplitude modulation to produce SSB. Suppose we have generated SSB at low level. We can envelope-detect it, amplify it, and use the amplified envelope to AM-modulate the class-C or class-D amplifier. At the same time we can phase-modulate the amplifier with the phase determined from the low-level SSB signal.

The low-level signal is simply amplitude-limited and then used to drive the modulated amplifier. Moreover, an existing AM transmitter can be converted to single-sideband by making only minor modifications.

At the receiver, the phase of the BFO selects one or the other. Note that the carrier can be suppressed, but retaining at least a low-power pilot carrier provides a phase reference for the receiver. Here, the receiver uses a narrowband filter to isolate the pilot carrier and then amplifies it to obtain a reconstituted BFO or LO, depending on whether the receiver is a superheterodyne or uses direct conversion to baseband.

In practice, carrier regeneration is almost always done with a phase lock loop. QAM: a transmitter; b receiver. The U. The QAM system of Figure 8. However, such a QAM stereo signal would not be compatible with the envelope detector in standard AM receivers. Several compatible analog systems were developed and used for AM stereo, but at this writing, both AM and FM stations are adopting compatible hybrid digital HD systems in which the digital signals occupy spectral space on either side of the conventional analog signal.

Demonstrate for yourself the kind of phase distortion that will occur when the BFO in a product detector does not have the same phase as the suppressed carrier.

Would you expect these waveforms to sound the same? This just inverts the waveform. Is this a special case or is an inverted audio waveform actually distorted? Problem 8. The phase-shift networks used in the phasing method of single-sideband generation have a flat amplitude vs.

Allpass filters have equal numbers of poles all in the left-hand plane and zeros all in the right-hand plane. Find the amplitude and phase response of the network shown below, which is a first-order allpass filter. Note that the inverting op-amp is used only to provide an inverted version of the input. The most general allpass filter can be obtained by cascading first-order allpass sections Problem 8.

Find the amplitude and phase response of the network shown below, a second-order allpass filter. They are used in large transmitters and industrial induction heaters, where high efficiency reduces the power bill and saves on cooling equipment, and also in the smallest transmitters, such as cell phones, where high efficiency increases battery life.

These amplifiers are so nonlinear the output signal amplitude is not proportional to the input signal amplitude , they might better be called synchronized sine wave generators. They consist of a power supply, at least one switching element a transistor or vacuum tube , and an LCR circuit. The LC network is resonant at the operating frequency. The output sine-wave amplitude, while not a linear function of the input signal amplitude, is proportional to the power supply voltage.

Thus, these amplifiers can be amplitude modulated by varying the supply voltage. Of course they can also be frequency modulated by varying the drive frequency within a restricted bandwidth, determined by the Q of the LC circuit. Finally, they can be used as frequency multipliers by driving them at a subharmonic of the operating frequency. The circuit looks no different from the class-B amplifier of Figure 3. But here the active device transistor or tube is used not as a continuously variable resistor, but as a switch.

To simplify the analysis, we consider the switch to have a constant on-resistance, r, and infinite off-resistance. This model is a fairly good representation of a power FET, when used as a switch. The switch has internal resistance i. Class-C amplifier operation. Normally the LC circuit has a high Q at least 5 so its flywheel action minimizes distortion of the sine wave caused by the abrupt pull-down of the switch and by the damping caused by the load.

The drive is shown as a rectangular pulse but is often a sine wave, biased so that conduction takes place just around the positive tips. Class-C amplifiers are normally run in saturation, meaning that the switch, when on, always has its lowest possible resistance, ideally much less than the load resistance.

With this assumption, let us analyze the circuit of Figure 9. The input power the power supplied by the battery must be equal to the sum of the output power the power dissipated in R plus the power dissipated in the switch resistance r.

The efficiency is given by the output power divided by the power supplied by the battery. Class-C efficiency vs. Evaluating the integral in Equation 9. This expression for efficiency is plotted in Figure 9. Note that this amplifier model, assuming a constant resistance in the switch, can be solved exactly by finding the general solution for the transient waveform during the switch-off period, as well as the transient waveform during the switch-on period.

Because the differential equations are of second order, these general solutions will each have two adjustable parameters. The parameters are found by imposing the boundary conditions that, across the switch openings and closings, the voltage on the capacitor is continuous and the current through the inductor is continuous.

Nevertheless, their nonlinear characteristics are specified graphically on data sheets, and accurate class-C analyses can be done numerically. The method is basically the same as the simplified analysis; one assumes the resonant LC circuits at the input and output have enough Q to force the input and output waveforms to be sinusoidal.

The power supply voltage times the average current gives the total input power. The difference is the power delivered to the load. The designer selects a device and a power supply voltage and assumes trial waveforms with different bias points and sine-wave amplitudes.

Usually several trial designs are needed to maximize output power with the given device or to maximize efficiency for a specified output power. The grid draws current and dissipates power. Data sheets include grid current curves so that the designer can use the procedure outlined above to verify that the chosen operating cycle stays within both the maximum plate dissipation rating and the maximum grid dissipation rating. When tetrodes are used, a third analysis must be done to calculate the screen grid dissipation.

But the usual way to put the tank at dc ground is to use the shunt-fed configuration shown in Figure 9. In the shunt-fed circuit, an RF choke connects the dc supply to the transistor and a blocking capacitor keeps dc voltage off the tank circuit. The RF choke has Figure 9. Equivalence of series-fed and shunt-fed circuits. Tetrode tubes have an additional grid, the screen grid, between the control grid and the plate. The screen grid is usually run at a fixed bias voltage and forms an electrostatic shield between the control grid and the plate [5].

The switch pulls pulses of charge from the blocking capacitor. This charge is replenished by the current through the choke. Figure 9. Note that the series-fed and shunt-fed equivalence applies as well to amplifiers of class-A, B, or C and for large-signal or small-signal operation. The class-C amplifier is therefore equivalent to a voltage multiplier which forms the product of a nearly unit-amplitude sine wave times the power supply voltage.

Modulating varying the power supply voltage of a class-C amplifier is the classic method used in AM transmitters. Note that this useful property of a class-C or D or E amplifier would be considered a defect for an op-amp circuit — poor power supply rejection. Of course there will be a greater voltage droop, producing less output power, but note that the circuit becomes a frequency doubler.

If the circuit is pulsed only on every third cycle, it becomes a tripler, etc. It is common to use a cascade of frequency multipliers to produce a high RF frequency that is a multiple of the frequency of a stable low-frequency oscillator. Class-D and class-E amplifiers can also be used as frequency multipliers.