In Amplifiers, Uncategorized

This is part 2 of this series. Part 1, Applications, is available here.

In this article we discuss amplifier figures of merit, and along the way you will hopefully develop an intuition for how to select an amplifier for your application based on a datasheet.

Figures of merit for microwave amplifiers fall into three categories:

Primary Function Factors Affecting Electrical Performance Factors affecting Usability or Convenience
Gain
  • Noise (noise figure/factor/temperature)
  • Phase noise
  • Gain Saturation (P1dB/Psat)
  • Nonlinear distortion
  • Harmonic generation
  • Multitone Harmonic distortion (IP3 & IP2)
  • Return Loss/VSWR
  • Reverse Isolation
  • Stability
  • Efficiency
  • Size
  • Packaging
  • Biasing Requirements
  • Cost

The above are amplifier specific figures of merit. There are closely related system level figures of merit that are defined throughout this article, but they typically will not show up on a datasheet. Passive components (power dividers, directional couplers) can be easily characterized with S-parameters and short datasheets since their parameters only change mildly with temperature and impedance, but not with power levels. Amplifiers are nonlinear devices, so each figure of merit will vary as the input power, bias, and signal characteristics change. Amplifiers are sometimes designed to operate in non-50Ω environments as well, so the full range of characterization data for them is much more expansive. Each figure of merit must be defined for a given set of conditions.

Primary Component Function

The primary function for a microwave amplifier is to increase the amplitude of the electrical signal, as quantified by the gain. Gain for a microwave amplifier refers to the ratio of output power to input power expressed in dB, specified at a given frequency, bias condition, and temperature in a 50Ω system. It is best measured on a calibrated vector network analyzer (VNA).  Gain is usually measured as ‘small signal gain’, where the input power level is low enough that gain is very weakly dependent on input power.

Factors Affecting Electrical Performance

Spur Free Dynamic Range (SFDR) refers to the ability of a system to detect both high power and low power signals; it is the ultimate measure of a systems performance. It is always limited by noise on the low power end and nonlinear distortion on the high-power end.

Noise figure (expressed in dB), noise factor (Unitless), and equivalent noise temperature (expressed in K) are different ways of quantifying the same effect: random signal fluctuations applied to the amplified output signal by the amplifier. In any system operating above 0 kelvin there will be random electrical signal fluctuations due to the thermal energy of the electrons. This noise and the desired signal are amplified by the same value of gain. Quantum processes in the transistors add further random fluctuations which manifest as noise on the output signal; noise factor measures the magnitude of these fluctuations added to a signal with input noise equal to the thermal noise floor. Noise figure expresses the same ratio in logarithmic units. Equivalent noise temperature expresses the temperature of a noise source that would produce the same amount of noise, and is dependent on the measurement bandwidth. The minimum detectable signal of a system is limited by the noise added by the system, which is limited primarily by the noise figure of the first stage amplifier in the receiver and any preceding loss.

Phase noise is a particular type of random electrical fluctuation that affects the timing (phase) of the signal. In amplifiers it arises from the upconversion of the intrinsic 1/f noise of the transistor used, from AM-PM noise, from white noise, and other sources. It is quantified as a power spectral density in dBc/Hz at a given offset frequency from the carrier. Phase noise is a limiting performance factor for highly sensitive radar systems that detect small frequency shifts. It affects the dynamic range only when signals close to the carrier need to be detected.

On the high end saturated output power (Psat) is the maximum RF/microwave power, expressed in dBm or Watts, the amplifier can produce for a given frequency, bias condition, and output load. In power amplifiers the output tuning is often optimized for output power and efficiency simultaneously. If a power level above Psat is injected into the amplifier, it will act as an attenuator and exhibit odd behavior (if it is not damaged).

As the input power increases the gain of the amplifier is gradually reduced until the saturated output power is reached. The input power that produces a gain of 1 dB less than the small signal gain is called the input 1 dB compression point (input P1dB, expressed in dBm) and the output power is called the output 1 dB compression (output P1dB, also expressed in dBm). Other common compression points are 3 dB, 5 dB, and 0.1 dB. For amplifiers compression points are usually expressed for the output rather than the input.

Typically only constant power amplifiers, such as single tone driver amplifiers) or phase modulated power amplifiers, are operated at or near Psat. Broadband signal amplifiers are usually limited by nonlinear distortion to power levels well below saturation, depending on the required signal integrity.

Nonlinear distortion occurs when the amplifier response shows a dependence on input power. There are many elements within the amplifier circuit that can show input power dependence (transistor capacitance is voltage dependent, for example). The most prominent nonlinearity, however, comes from gain saturation.

For a single tone input, gain distortion causes even and odd harmonic generation (quantified as harmonic suppression in dBc, sometimes called HD2, HD3). For multiple tones or a broadband input signal, gain distortion causes multitone harmonic distortion, which is typically quantified as IP3 and IP2 in dBm for the amplifier on its own.  Many other system level metrics for nonlinear distortion are defined and explored at the end of this article.

Factors Affecting Convenience and Usability

Unlike the previously discussed Figures of Merit, the following will not necessarily affect the dynamic range of the system, but they are factors that must be considered by the system designer. First are the factors that are common to all RF/microwave components: return loss and VSWR. Return loss is the ratio of incident to reflected power at either port (expressed in dB) and VSWR is the linear ratio of peaks and valleys in the resulting standing wave pattern. Both numbers express the same amplifier characteristic in different ways, a characteristic commonly referred to as ‘match’ to the system reference impedance (commonly 50 or 75Ω).

The match of broadband linear signal and driver amplifiers is typically not as good as passive components such as power dividers, but better than mixers. Values of 10-15 dB return loss or 1.4-2:1 VSWR are reasonable. Transistors are highly reactive elements that are difficult to match over a broad bandwidth, although very good match can be achieved over a narrow band. Power amplifiers and low noise amplifiers have different issues. As mentioned in part 1, LNAs are deliberately mismatched from 50Ω to prevent noise from being delivered into the input. Similarly, PAs are matched more for efficiency and power output than for return loss.

Reverse isolation refers to the insertion loss of the amplifier in the reverse direction, measured in dB. In the small signal model of a transistor, the only conduction path from the drain/collector to the gate/base is through a small capacitance. This means that isolation starts out very good at low frequencies but degrades at high frequencies. Amplifiers are frequently used as buffers to provide isolation between stages in an RF system as an attractive alternative to bulky magnetic isolators.

Here it is worth mentioning that both broadband output return loss and isolation are particularly important for LO driver amplifiers. Since a mixer acts as both a multitone source and load at all three ports, the LO port will generate tones across a broad bandwidth. If the output return loss of the LO buffer amplifier is good, these will be efficiently absorbed and not cause problems. Otherwise they could reflect and create standing waves and conversion loss ripple. Similarly, if the isolation is poor, then the tones will pass through the amplifier to the LO source, potentially mixing and creating unwanted harmonics from the LO source.

Half of the art of amplifier design is in meeting electrical performance criteria, and half is in maintaining stability.  To create an oscillator all you need is a noise source and an in-phase feedback loop with unity gain. Noise and gain are always present in a microwave amplifier, so feedback paths must be carefully controlled to prevent undesired or parasitic oscillation. There are three common feedback paths

  • Reflection from the output back into the amplifier, which depends on the amplifier load
  • From the output of the amplifier to the input of the amplifier, either radiatively or through stray transmission lines
  • From the output back through the transistor bias lines

The first feedback path can be mostly designed for by guaranteeing unconditional stability. An amplifier is unconditionally stable if it will not oscillate under any passive loading, that is as long as there is not a gain on the reflection back to the amplifier. This can be designed for with a pair of inequalities known as the Rollett criteria for unconditional stability (using K factors), and it is frequently a feature of both linear signal amplifiers and driver amplifiers. Often a power amplifier is conditionally stable, where it will not oscillate as long as the source and particularly the load impedances fall within a certain range of acceptable values. It is important not to power up a conditionally stable amplifier with an open circuit, or it could oscillate and damage the amplifier.

The next two feedback paths can be designed for on-chip (for a MMIC amplifier), but they depend on the complete amplifier operating environment, including bias lines and packaging. Insufficient isolation typically occurs at very high frequencies where radiation effects are higher or very low frequencies where isolation is more difficult to achieve (bypass caps are not as effective).

This means that while stability can be designed for, it is very difficult to prove experimentally. Oscillation tends to occur at very low frequencies where the transistor gain is high (and below measuring equipment ranges) and at very high frequencies where radiation effects are more pronounced (and again above measuring equipment ranges). Oscillations may be present internally to the amplifier, but not appear outside the amplifier circuit since it may be blocked or filtered. When the DC power consumption fluctuates unexpectedly, unexpected spurious products appear in the output of the amplifier, output power is high without an input, or an amplifier is very sensitive to its environment, these are all indications of a stability problem with the amplifier. Special care should be paid to the bias network and minimizing cavity Q of an amplifier operating environment, as this provides a likely feedback path for low frequency oscillations.

Another factor unique to amplifiers is efficiency, which is expressed in many different ways, but the most common and relevant is power added efficiency (PAE). PAE is the ratio of added RF power (RF output power minus RF input power) to DC power, expressed as a percentage. For amplifiers with high gain such as LNAs, the PAE will be very close to the drain efficiency, which is the ratio of output RF power to DC power. Efficiency is important for several reasons. Obviously for mobile applications efficiency determines the battery life of the system. For airborne or space based systems the total power can be limited by the power generation capability of the platform, and the range is determined by the output power of the amplifier, so the range is effectively determined by the efficiency of the power amplifier.

The most common efficiency concern for all systems, however, is heat dissipation. All RF and DC power input that is not output as RF power is dissipated as heat. Heat is the mortal foe of the amplifier. Due to the physics of transistors, amplifiers are more efficient, have lower noise figure, and have higher gain at lower temperatures (this also makes them more likely to oscillate at low temperatures). As the temperature increases, the reliability of the amplifier is degraded, as expressed by the mean time to failure. As the temperature increases, the mean time to failure decreases exponentially. This heat also affects the reliability of all surrounding components. For this reason highly efficient power amplifiers are desired to reduce the cooling requirements of densely packed systems even in land based applications where power is abundant and cheap.

It is important to note here that DC power consumption is a function of input power. As the input power increases the DC power consumption will typically increase, but the RF ouput power increases even faster, leading to an increase in efficiency. PAE is usually highest when the amplifier is heavily compressed. When considering the efficiency, current consumption, or heat dissipation of an amplifier it is important to consider the input power that will be seen by the amplifier and record the DC current at that input power and frequency.

Efficiency is closely related to power, which is the P in the acronym SWaP, for Size, Weight, and Power. SWaP is largely determined by the package that an amplifier comes in. While all of the above considerations apply to all microwave amplifiers, these amplifiers can come in packages that range from a tiny chip to a complete rack mounted system. The most common microwave amplifiers by volume are integrated CMOS amplifiers in RFICs. There are many amplifiers available either as bare die or encapsulated in high performance ceramic or low cost plastic surface mount packages. Other amplifiers come as surface mount transistors combined with matching and biasing elements on a surface mount circuit board.

Packaging is one of several other convenience factors that can end up being deal breakers for certain applications, even when electrical performance must be sacrificed. Small packaging is required for certain form factors (like handsets), and sometimes this requires exotic chip scale packaging such as flip chip. Exotic packaging can save size, but requires advanced PCB and assembly techniques, which can make an amplifier product less usable for most customers. The easiest package to use is typically that which is compatible with standard surface mount reflow conditions.

Different transistor technologies have different biasing requirements, which can be a serious convenience factor. The highest performing transistors for many applications are depletion mode, which means that they are normally ‘on’ unless a negative bias is applied. This means that negative voltage generation and sequencing is required, which can involve a complex circuit that adds to the size, cost, and complexity of a system. Some transistors can be operated safely with a grounded gate (such as the ADM series) meaning that negative biases are optional and sequencing is not required. Still other transistor technologies (such as HBTs and enhancement mode transistors) are normally off, meaning that a negative bias is not required at all and the positive bias provides the biasing. Depending on the application this may involve performance tradeoffs.

This brings us to our last consideration, cost. The lowest cost, most ubiquitous microwave amplifiers are plastic packaged wireless communications chips in handsets, and they are almost always integrated in multi-chip modules with other functionality such as filtering and switching, and sometimes they are integrated on the very same die. The reason that the cost is so low for these components is not the fabrication technology or even the packaging, but the volume. Volume is easily the single most important factor in the cost of an amplifier. Complicated multi-chip modules can be produced for a few dollars, while even basic custom designs can cost many thousands of dollars, due to the economics of volume production. Amplifier require significant investment to design and qualify from a reliability standpoint. The tooling cost of producing these amplifiers (dominated by mask costs) is at least six figures (in 2020 US dollars), and can be over $1M for silicon designs.

This concludes our discussion of the figures of merit for an amplifier. Hopefully this has given you a basic understanding of the factors that you should be on the lookout for when designing your microwave system. For each of the factors mentioned in this introduction you can find many, many references publicly available. In our next installation we will discuss basic microwave amplifier circuits.

Distortion Effects in Amplifiers and Microwave Systems

Here we will illustrate how different nonlinear distortion effects arise from basic gain saturation in an amplifier. As mentioned above amplifier nonlinear distortion is typically quantified only by P1dB, IP2, IP3, and harmonic generation. However, there are many other system level specifications that arise from these basic distortion effects that we will discuss here.

First consider a single tone into an amplifier with a simple saturation characteristic. This amplifier saturates symmetrically, with constant gain below ±0.5V and constant output voltage above or below that.

When a small signal single frequency tone is amplified, the output is a scaled version of the input and the frequency domain contains only the single input frequency. When the input is a larger amplitude tone the amplifier ‘clips’ the upper and lower portion of the signal, creating more of a square wave. In the frequency domain there are additional tones at 3f, 5f, 7f, and all other odd harmonics. The takeaway is that symmetric compression creates odd harmonics.

Note that fundamental power continues to increase after the signal begins to compress, but flattening comes from additional power being added in higher harmonics.

Next we’ll look at an amplifier that has linear gain for all negative voltages, and only saturates on the positive side, as in a class-AB amplifier:

Again a small signal is amplified correctly, but a large signal clips asymmetrically. In the frequency domain you now see harmonics at 2f, 4f, and other even harmonics in addition to odd harmonics. Two takeaways from this:

  • Asymmetric amplifier saturation causes even order harmonic distortion, manifest as duty cycle distortion in the time domain
  • Amplifier harmonic distortion and generation is dependent on bias conditions

Now consider an amplifier with two equal power tones at frequency f ±δf with a small frequency difference between them as the input. When two equal power tones with different frequencies combine they create a ‘beat’ signal which has periodic nulls and peaks with twice the voltage of either signal alone.

The peaks are cut off, even though the amplitude of both signals is much lower than what was required to cause harmonic distortion in the CW case. This is called two tone intermodulation distortion, which is a particular method to quantify multitone intermodulation distortion. This distortion creates sidebands  at f ±2δf that are very near the signal and difficult to filter out. These sideband tones are called third-order intermodulation products, and the ratio of the power in the sideband tones at f ±2δf to the carrier is referred to only as IM3; it is expressed in dBc and specified at a given fundamental tone output power.

Similarly, a tone generated at 2f is called the second-order intermodulation product. The ratio of this tone to the desired fundamental is called IM2 and also expressed in dBc for a specified input power. Typically the input power invariant output third order intercept point (OIP3) and output second order intercept point (OIP2), both expressed in dBm, are used instead. The meaning of these values is described many other places, so we will not discuss it, but the formulas are included here for convenience, where all values are in dBm or dBc and PO refers to the output power of one of the desired tones:

Consider one more example where instead of two tones, we have four tones:

Again the peaks are even larger than they would be for a comparable two-tone input, and so the input signals must be reduced even more to maintain linear signal amplification. For more complex signals with more tones, or for amplifiers that must simultaneously amplify multiple signals, the peaks can be even larger. While the cause is a voltage phenomenon, this is usually expressed as the peak to average power ratio (PAPR), expressed in dB, which as the name suggests is just the ratio of the peak power in a modulation format to the average power. For a two tone signal, the PAPR is 3 dB, for a four tone signal it is 6 dB. The amount that the input signal must be reduced to maintain linear amplification is called backoff, expressed in dB, and is typically slightly more than the PAPR.

The major challenge of modern wireless communications is limited bandwidth, which drives up the cost of even small chunks of the spectrum to billions of dollars. The solution has been to use more advanced modulation formats (such as code division multiple access (CDMA) and orthogonal frequency division multiplexing (OFDM)) that efficiently spread power across the entire spectrum. These formats maximize the data capacity of the bandwidth by creating a signal that appears very similar to random noise (a single frequency tone carries no information). This random appearance also means that the PAPR is very high, which shifts the burden largely to the power amplifier to provide linear amplification to this complex signal.

The square shaped spectral formats of CDMA and OFDM give rise to a broadband intermodulation distortion referred to as spectral regrowth, which is quantified in a variety of ways. This is the equivalent of many IP3 tones occurring simultaneously, and like IP3 the intermodulation products appear both as noise on the signal and power leakage into adjacent frequency channels. The ratio of power in the main tone to the power in the adjacent channels is called the adjacent channel power ratio (ACPR), and it is defined in a given bandwidth. Spectral regrowth, ACPR, and another common measure of signal quality called error vector magnitude (evm) are measured for a given modulation scheme, and therefore are system level specs. Only IP3 and IP2 are given as amplifier component specs. It is important to note that unlike real noise, spectral regrowth and IP3 are deterministic, which means that they can be compensated for with pre-distortion or signal cancellation.

Now let’s look at what saturation looks like in a real broadband driver amplifier, the ADM-0012-5931SM. This is an efficient, low power amplifier, with correspondingly low P1dB and IP3.

As the amplifier approaches saturation, the signal becomes distorted by the voltage variable gain, and nonlinearities are observed. As you can see in the above plots, the ADM-0012-5931SM has a lower P1dB relative to its Psat when biased at 3V drain bias vs. 7V gate bias. This means that nonlinearities appear at lower input power levels with the lower bias condition, which is indeed what we see when we look at the harmonic generation (one type of nonlinearity):

What do these nonlinearities look like on the signal in the time domain? This depends on many factors, including how much bandwidth the amplifier supports. An ideal broadband amplifier will saturate by simply clipping off the ends of the output signals, but this creates a fast transition that requires higher order harmonics to be supported. This is almost exactly what we see when we drive the ADM1-0026PA at 3 GHz, where it can support much higher frequency harmonics. This effect is desirable and exploited with a commutating mixer such as the T3 mixer series (this is detailed in the T3 mixer primer). Ironically the non-linearity of the amplifier helps create a more linear mixer.

 

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