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Amplifier Fundamentals

From “Handbook of RF, Microwave, and Millimeter-Wave Components” by Leonid A. Belov, Sergey M. Smolskiy and Victor N. Kochemasov by Artech House

July 30, 2018

The main role of a microwave amplifier is to increase the level of an input signal (e.g. an oscillation span, amplitude, or power) without introducing noticeable distortion in the signal waveform, its spectral composition and the ratio of a signal to noise at the input. Any processing of a signal introduces unwanted distortion of some level. With signal amplification there is frequency distortion, nonlinear distortion, and interference. In linear circuits, frequency distortion is caused by signal transformations in which reactive parameters are not dependent on signal amplitude. Non-linear manifestations are varied. Among them are intermodulation distortion caused by the interaction of spectral components of one modulated signal and cross distortions are caused by the interaction of modulation components from several signals within a frequency bandwidth. Interference, which appears at the amplifier output, can be additive (instantaneous values of interference summed with instantaneous values of the signal) or multiplicative.

Figure 1

Figure 1. Diagram of an amplifier stage.

An amplifier is represented in Figure 1 as a black box with an input signal uin(t), an amplified output signal uout(t) and a power supply E0. Assume that the input is a single-frequency unmodulated sinusoid or a sum of two sinusoidal signals of equal amplitude U1 with closely spaced frequencies f1 and f2:

 

                        uin1 (t) = U1sin(2pf1t)   or

                        uin2 (t)  U1[cos(2 pf1t) + cos(2 pf2t)]                     (1)

The value of U1 can be found using the input power Pin with a known input impedance Rin as

U1 = (2PinRin)1/2                                          (2)

By default, one can assume Rin = 50 ohms.

We can also assume that the amplifying active element is nonlinear and inertia-free; it creates an output with frequencies +mf1 +nf2 (coefficients m and n are arbitrary integers). The amplitudes of these spectral components depend only upon the amplitude of the input signals and the coefficients of nonlinear conversion. Components of the third order with frequencies 2f1- f2 and 2f2-f1 appear in the spectrum structure of the output signal near frequencies f1 and f2. The power of these intermodulation components is proportional to U1 3 (see Figure 2).

Fig 2
     Figure 2. Amplitude characteristics of double-tone signal intermodulation products.

While the power of the output spectral components of the first order with frequencies f1 and f2 increase with input power at a 10 dB/decade slope (i.e. linearly), the components of the third order increase at a 30 dB/decade slope. In the absence of saturation (i.e. by extrapolating their log linear small signal input/output relationships), powers of the first and third order products are equal at the third order intercept point (IP3). The value of PinIP3, or equivalently PoutIP3, characterizes the level of an amplifier’s nonlinear distortion. At increased values of Pin, saturation limits the Pout/Pin dependence in a transistor amplifier. In microwave tube amplifiers (e.g. travelling wave tubes (TWT) and klystrons), when Pin exceeds Pin satPout decreases.

The value Pin1dB, and equivalently Pout1dB, at which compression at the output does not exceed 1 dB, is widely considered to be a conditional boundary for maximum signal level in a linear mode. The level of background power of the amplifier’s inherent noise reduced to the input (i.e. the noise floor) defines the lower boundary of the amplifiers dynamic range.

Efficiency of a power amplifier η = Pout/Pdc is the ratio of microwave output power Pout to power consumed by the DC power supply. For transistor amplifiers with insufficiently high gain, G = Pout/Pin, it is more accurate to use power added efficiency PAE = (Pout - Pin)/Pdc, which subtracts the power contributed by the preceding stage(s). The relationship between these measures can be expressed by:

                                                PAE = η (1-1/G)                     (3)

To characterize the mode of an RF transistor power amplifier (PA), one can use the designation of classes from A to F.  We introduce the current conduction angle q in the input circuit, which is the normalized characteristic of the input signal amplitude U with respect to the difference between the current cutoff DC voltage E’ and the bias voltage Ebias.

                                              cos q ~ -(Ebias – E’)/U             (4)

Class A (see Figure 3) corresponds to small signal operation in the linear region of the transistor’s input characteristics. Class AB corresponds to operation with a cutoff angle from 180 to 90 degrees, Class B corresponds to operation with a cutoff angle near 90 degrees, and the Class C mode corresponds to operation with cutoff angle from 90 to 0 degrees.

Fig 3
     Figure 3. Transistor amplifier classes.

Switching modes of radio frequency amplifiers enable PAE increases up to 70 to 90 percent, but for comparatively low frequencies up to 1 GHz. Quasi linear Class C operation for high frequency PAs also enables a PAE increase; however, its compression characteristic is non-monotonous (see Figure 4).

Fig 4
     Figure 4. Class A and C amplification compression characteristics.

Classification and Parameters

There are many varieties of amplifiers for RF and microwave applications. Figure 5 illustrates one way of classifying them. There are several key elements, which include the operating frequency band, small-signal gain G0, maximum output power Pout max, active element technology, the design solution and the level of nonlinear transformation products. Amplifiers may be designed and optimized for power or efficiency. Cascaded amplifiers have similar values of input and output impedance (typically 50 ohms) and are connected in series so that the total gain expressed in decibels is equal to the sum of the individual stage gains. In gain control amplifiers (GCA; some manufacturers use the abbreviation VGA-variable gain amplifier) gain is changed by an external analog or digital signal. High linearity amplifiers have wide linear dynamic ranges, while limiting amplifiers are designed to saturate in order to reduce spurious variation of the input signal power.

Fig 5
     Figure 5. Radio frequency amplifier classifications.

When evaluating maximum output power of an amplifier, one must take into consideration its operating frequency. Device geometric dimensions decrease with increased operating frequency. Surface and volumetric energy density grows, introducing heat dissipation limitations. The level of amplifier output power is thus inversely proportional to the square of the operating frequency for a given device technology and thermal design. The summation of power from several active elements allows growth of the output power level but complexities arise with construction, energy efficiency of power splitters and combiners, phase synchronism of summed channels and prevention of spurious self-excitation. Because of these factors, for the decimeter wavelength range (frequencies up to 3 GHz), the conditional boundary of the high power stages is 100 W, for a portion of the centimeter range (frequencies up to 30 GHz) it is 10W, and for frequencies above 50 GHz more than 1W may be considered a high power.

A bidirectional amplifier amplifies the power of a source signal to be transmitted by an antenna transmitter signal, while a signal received by the antenna through the same connections passes to a low-noise amplifier and then to a receiver.

A transimpedance amplifier converts an input current into a voltage. It is used, for example, to match the output impedance of an RF input to a fiber-optical communication line with the input impedance of a laser diode or the output impedance of photodetector with the input impedance of a microwave section.

Special-purpose amplifiers are designed for specific communications standards (e. g. GPS, IEEE 802.11, WiFi, WLAN, 64QAM). Front ends include low-noise preamplifiers in combination with the frequency downconverters prior to baseband processing.

The logarithmic (log) and antilogarithmic (antilog) amplifier, variants of operational amplifiers (op-amp), are nonlinear circuits, in which output voltages are proportional to the logarithm (or exponent) of input voltages. Such amplifiers are used in intermediate frequency sections for compression (or extension) of the input power dynamic range, or for automatic gain control. For a logarithmic amplifier, the input signal amplitude interval (from Vin,min to Vin,max) is transformed at the output to:

                                                     Vout = -K ln [Vin/Vref]                            (5)

where K is a constant coefficient and Vref is a reference voltage.

The technology for the active element defines power supply parameters and the amplifier application. For solid-state amplifiers, besides silicon bipolar transistors (BT), new technologies have been developed around materials and structures such as SiGe, GaAs, GaN, InGaP, LDMOS, pHEMT, AlGaAs/GaAs, HFET, and pHEMT.

To provide high and ultrahigh output power in the microwave range, power amplifier tubes, such as klystron amplifiers, and traveling-wave tube amplifiers (TWTA) with different variants of slow wave structures are used.

Consider the following parameters:

  • Operating frequency range with boundaries flow and fhigh.
  • Small-signal gain G0 = Pout/Pin; voltage gain GVO = Vout/Vin, or small-signal power gain GPO = Pout/Pin; when using the logarithmic scale numerical values of GVO = 20log10 (Vout/Vin) in dB and GPO = 10log10 (Pout/Pin) dB in dB for the same input and output impedances.
  • Noise figure (NF).
  • Maximum output power of a linear amplifier Pout1dB.
  • Maximum output power in saturation Pout sat.

There are no generally accepted low flow and high fhigh boundaries for an amplifier’s operating frequency band. One may specify by default such frequency values as cutoff frequencies at which the gain G0 decreases by 3 dB compared to the value in the middle of the operating frequency band. The absolute frequency bandwidth (BW) = fhighflow defines the range over which distortion of input signals is within an acceptable range for an application. The relative frequency BW kf = 2(fhighflow)/(fhigh+flow): for narrowband amplifiers kf << 1;  for octave amplifiers kf ~ 2 and for multi-octave amplifiers kf > 2. For some models one may specify direct current (DC) as a lower bandwidth boundary so that in this case the kf value loses its sense. In these cases the value of the low cutoff frequency flow is defined by the frequency properties of bias circuits and blocking elements.

For wideband amplifiers the maximum gain flatness in the operating frequency band is specified. In some applications (for instance, for compensation of the frequency dependence of the other elements in a chain) amplifiers are designed with a given (positive or negative) slope value Sf = dG0/df for the amplitude-frequency characteristic in the operating frequency band.

For amplification of a bandpass signal there may be distortion caused by deviation  from  a  linear  phase  characteristic:  the  function  f(f)  of  the phase shift f = fout  – fin  in the amplifier with respect to a carrier frequency. As the quantitative characteristic of this phenomena we can use the non-uniformity of the signal group delay  tgr  = | df/df | in the operating frequency band.

An amplifier’s noise properties are defined by its noise factor Fnoise, which indicates how much the power spectral density (PSD) of the amplifier’s inherent noise exceeds the PSD of a resistor with resistance equaled to the input stage resistance. The noise temperature in Kelvin

                                      Tnoise = T0 (Fnoise – 1)                                        (6)

is called the amplifier noise temperature, where T0 = 290 K is standard (room) temperature. As a noise amplifier characteristic one most often uses the noise figure (NF) expressed in decibels

                                                NF (decibels) = 10log10Fnoise                                    (7)

For amplifiers dedicated to processing sinusoidal reference signals, we may specify values power spectral density (PSD) of the amplifier phase noise Sj(F) at different frequency offsets F near the carrier frequency, which increases the total level of a system’s output signal phase noise. Typical values at 10 GHz are -145 dBc/Hz at an offset of 100 Hz from the amplified signal with a white noise noise level of 170 dBc/Hz at an offset of 1 MHz and beyond.

PinIP3 is used for quantitative estimation of amplifier nonlinear properties (i.e. intermodulation distortion (IMD)). Alternatively PoutIP3 may be specified. The OIP3 value is expressed in dBm, it exceeds the Pout1dB value, and corresponds to an inadmissible level of distortion. For high power microwave amplifiers it is necessary to take into account amplification compression characteristics (AM/AM compression) and amplitude-phase conversion characteristics (AM/ PM conversion).  

Sensitivity in a receiver is normally taken as the minimum input signal (Pin min) required to produce a specified output signal having a specified signal-to-noise (S/N) ratio. Dynamic range of an input signal level for a linear amplifier is the following ratio expressed in decibels:

                                                D = 10 log (Pin 1 dB/Pin min)                               (8)

In a linear mode, an amplifier’s frequency-dependent complex S-parameters can be measured. One may also use X-parameters of power amplifiers, which are a generalization of S-parameters, taking into account the amplitudes of input and output signals.

Sensitivity of gain to supply voltage variations can be characterized by a variation of G0 in decibels per volt of supply voltage and sensitivity to environment temperature variations by variation of G0 in decibels per degrees Celsius.

The following additional characteristics are also important: weight; dimensions; mounting arrangement; input, output and bias connections; rated impedance of input and output circuits; and sensitivity to the environment: vibration, shock, moisture, radiation level, and static electrical and magnetic fields.



TYPES OF AMPLIFIERS

Low-Noise Amplifiers

Low-noise amplifiers are used in input circuits of amplification stages for small signals mixed with noise in a limited frequency band. Amplifiers with NF less than 5 dB are usually considered low-noise amplifiers. For amplifiers in the millimeter-wave range (frequencies greater than 30 GHz) they may be considered low-noise with NF less than 15 dB. The achievable value of NF depends, to a large degree, upon an amplifier’s high cutoff frequency fhigh, output power Pout1dB, and environmental temperature. Characteristics of some models with low level of inherent noise are presented in Table I.

Table I

High Dynamic Range Amplifiers

Nonlinear phenomena with a growth in signal level are unavoidable in microwave amplifiers. If the signal is modulated in phase, frequency, or amplitude; then, as a result of intermodulation distortion of the third and fifth order, spectral components appear in the operating frequency band that cannot be eliminated in further stages with the help of frequency filtering. Dynamic range can be characterized as the amount by which the value of PoutIP3 exceeds the level of intrinsic noise; therefore to extend dynamic range, one can decrease the inherent noise level (i.e. NF) while simultaneously increasing PoutIP3. The linear figure of merit

                              LFOM = PoutIP3/Pout1dB                         (9)                         

is used by manufacturers to compare the linearity of various microwave amplifiers. Parameters of some high dynamic range amplifiers are shown in Table II.

Table II

Solid-State Power Amplifiers

Identifying an amplifier as low, medium or high power is ambiguous: it is necessary to take into consideration the operating frequency and given manufacturing technology. Moreover, for high-power amplifiers the developer often faces limitations due to efficiency. For high power solid-state amplifiers, the most important parameters are Pout1dB, PoutIP3 and PAE. Parameters of some microwave solid-state amplifiers of medium and high power are listed in Table III. It should be noted that most manufacturers offer a wide range of products with different power levels for the same frequencies; the most typical examples are shown in the table.

Table III

Wideband Solid-State Amplifiers

Amplifiers of microwave signals with a wide (on the order of an octave) bandwidth and with the multi-octave bandwidths are used in ultrawideband (UWB) communication and in information transmission systems. Examples are presented in Table IV.

Table IV

Tube Amplifiers - Klystrodes, Klystrons, TWTs, Amplitrons, Crossed-Field, and Gyro- Amplifiers

For RF power less than 1W in the frequency range 0.3 to 10 GHz, engineering solutions using surface mount or integrated solid state semiconductor technologies are typically used. They provide a gain of 15 to 20 dB in a single stage (up to 60 dB with cascading), PAE of 45 to 60 percent, passbands of 0.1 to 5 GHz, noise figures of 0.5 to 5 dB, and the dynamic ranges of not less than 30 to 40 dB. For medium power level devices there are engineering and economic tradeoffs between solid-state and microwave tube solutions.

In complex signal chains, one might find some stages implemented with solid-state components, while other parts employ vacuum tubes. Very high power and amplifiers and oscillators are implemented, as a rule, with vacuum tube microwave electronics.

The engineering requirements for amplifiers of medium and high power are a compromise of   parameters such as linearity, gain, output power level, efficiency (PAE), bandwidth, weight and physical dimensions. One must also consider prime power needs, a means for air or water cooling and durability under expected environmental conditions such as temperature, pressure, moisture, shock, vibration and ionizing radiation. Some of these requirements can be better met with vacuum devices.

The modern multibeam construction of vacuum power amplifiers provides high and super-high output power. Tube active elements demonstrate markedly higher durability with respect to radiation. Although it is typical for traditional vacuum tubes to require power supplies with tens of kilovolts, it complicates (but does not exclude) their application in on-board and satellite equipment. Vacuum active elements of power microwave amplifiers are manifold.

A tetrode is an RF tube with a heated cathode, a control grid, a suppressor grid, and an anode. The tetrode is used as an amplifier of signal power for input signal frequencies from DC to frequencies where electron inertia becomes a limitation.

In the floating-drift klystron, electron inertia is used for bunching electron bundles during their transit between the input cavity gap and output cavities. Thus, the klystron is designed to amplify in the microwave range. For single-beam two-cavity or multicavity klystrons typical values of output power in continuous-wave mode achieve 50 kW at a gain 50 to 60 dB in a 10 percent relative frequency band. Multibeam klystrons utilize the oscillation excitation simultaneously in a set of from 8 to 36 beams, for which output power is summed.

A klystrode, or inductive output tube, represents a combination of a tetrode and a klystron: the input electron flow is modulated in density as in a tetrode and in velocity as in the klystron, while power is extracted much like a klystron. In such devices, PAE and linearity are essentially increased at high power, which explains its wide application in TV transmitters in the decimeter wavelength. In multibeam klystrodes the required supply voltages are reduced and realization of control grids becomes easier.

Traveling wave tubes (TWTs) can achieve 200 W using small diameter slow wave structures at frequencies from 10 to 25 GHz and with PAEs up to 60 percent for relative wide bandwidths of 1 to 2 octaves and the lifetimes up to 150,000 hours. TWTs with periodic slow wave, versus spiral, structures enable higher operating frequencies and PAEs, but with reduced the frequency bandwidth. In  a multibeam TWT it is possible to reduce the supply voltages for a more compact construction.

An amplitron is an amplifying device that employs the principles of a magnetron with crossed electrical and magnetic fields and is more commonly called a crossed field amplifier (CFA). It provides a high PAE (up to 90 percent) and extremely high power due to frequency synchronization of the output oscillation to an external narrow-band input signal..

In gyrotron amplifiers the hollow screw-shaped electron flow and continuous interaction with the traveling wave tubes (as in TWT) are used. This provides electronic efficiency up to 70 percent in the millimeter wavelength range with the power up to 100 kW within tens of seconds. Experimental models of power amplifiers such as gyro-klystrons, gyro-twystrons, and gyro-TWTs are offered in the microwave and terahertz ranges.

A comparison of parameters of power vacuum amplifying devices in the UHF range is presented in Table V.

Table V

Pulse Amplifiers

Amplifiers intended for amplification of pulse microwave signals (pulse amplifiers) or for pulse modulation of low-power continuous-wave signals (pulse modulated amplifiers) differ in their requirements for high instantaneous bandwidth. Instantaneous bandwidth determines the duration of pulse rise and fall edges, and often employs saturation. For a normal amplifier, the approximate rise/fall time is equal 0.35/(3 dB-BW); however, if a sharp filter is used, rise and fall times can be roughly halved.

Phase linearity (group delay variation) must be quite good without resonances or sharp variations. To limit the overshoot of a square pulse Bessel filters are sometimes used.

The development of pulse RF amplifiers has progressed in several directions to meet different needs. First, highly efficient amplifiers operating in the Class D switching mode close to saturation (see Figure 3) have been improved. Second, wideband pulse video amplifiers have been developed for optical laser modulators in communication lines, which have bandwidths from DC to several tens of gigahertz. Third, for radar, measuring systems, and UWB applications, it is necessary to have radio frequency pulse amplifiers with a small (from 3 to 10) number of periods of carrier RF oscillation per pulse duration, high (up  to hundreds of kilowatts) peak power and low duty factors.

Intermodulation Distortion and Linearization of Power Amplifiers

Figure 6

Figure 6. Predistortion digital linearizer.

For the retransmission and power amplification of microwave signals in wideband amplifiers with frequency channel division the challenge is to provide high efficiency with low intermodulation distortion. There are three main methods of power amplifier linearization: predistortion, feedforward and feedback.

 

The predistortion linearizer is implemented in the form of a serially connected controllable attenuator and phase shifter or a vector modulator.  It is connected to the input of the power amplifier being linearized. It makes amplitude and a phase changes to the PA input signal based on a table of stored corrections to the nonlinear AM/AM and AM/PM characteristics of the amplifier (see Figure 6).

 Feedforward linearization is accomplished by summating the main PA output of the amplified signal with a correcting signal from an auxiliary amplifier (AuxPA) (see Figure 7). The AuxPA input signal is created by comparing the input and output signals of the main PA in amplitude and a phase.

Fig 7
     Figure 7. Feed forward linearizer.

The feedback linearizer samples the PA input and output, and feeds back a correction to the input in order to cancel nonlinearities (see Figure 8). Demodulation of the input and output signals is enabled by a reference local oscillator (LO) tuned to the carrier frequency. Quadrature I/Q components of the baseband signal are compared and with a vector modulator connected to the power amplifier input.

Fig 8
     Figure 8. Cartesian feedback linearizer.

Related Publications

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