## 1 dB compression point

Defines the output level at which the amplifier’s gain is 1 dB less than the small signal gain, or is compressed by 1 dB (P_{1dB}).

NOTE: Most amplifiers start to compress approximately 5 to 10 dB below P_{1dB}. Applying signal power levels above this point results in a decrease in gain – therefore, the change in output power will not be linear with respect to a corresponding change in input power to the point where the amplifier is at saturation (P_{SAT}) and the gain equals zero.

Operating at output levels above P_{1dB} is not a normal operation for a linear amplifier.

## Conditionally stable

A conditionally stable amplifier refers to an amplifier which will oscillate under particular load or source impedance (VSWR) conditions, an undesirable situation. (See **Unconditionally Stable.**)

## Cp (Process capability)

Process capability is broadly defined as the specification width (S) divided by the process width (P) and is an indication of the spread of the process. Specification width “S” is the difference between the upper specification limit (USL) and the lower specification limit (LSL). Assuming the process to be Gaussian, its standard deviation can be denoted by sigma (σ).

## Process width

Defined as six times sigma (three sigma on each side of the mean). For example, if the USL and LSL of noise figure of an amplifier are 6.9 and 6.0 dB, then S is 0.9 dB. If the standard deviation is 0.1 dB, then P is 0.6 dB. Cp, the process capability, is 0.9/0.6 = 1.5

When Cp is 1, then 99.73% of the units pass specs and the process produces 0.27%. defective units. When the value of Cp increases, the number of defects decreases dramatically. Percentage defects is no longer a convenient measure at higher values of Cp; instead, parts per million (PPM) is used to describe the defect rate. For example, when Cp is 1.5, defects are 5 PPM and when Cp is 2 the defects are 0.002 PPM. In this last example (Cp = 2), process width is ± 6σ and the process is called a 6σ process.

All the above numbers are based on the assumption that the center of the spec limits and the center of the process are the same. When this not true, Cp does not provide complete information.

## Cpk (process capability of a non-centered process).

Cp does not take into account non-centering of the process and therefore is of minimal value in practice. In the general case a quantity called Cpk is used, which takes into account any non-centering of the process. Two equivalent definitions of Cpk:

In the Cpk definition NSL is the nearest spec limit, x-bar is the mean of the process, and the vertical lines (denoting absolute value) indicate that Cpk is always a positive number. Cp and Cpk are equal for a centered process. Cpk is also useful for defining processes with single-sided specifications. For example, noise figure of an amplifier has only an upper spec limit and active directivity has only a lower spec limit. In deriving Cpk, one should make sure that x-bar has a meaningful value, such as its being between spec limits when both spec limits are present. For singlesided specs, x-bar should be below the upper spec limit or above the lower spec limit. The graph at the side shows the number of defectives for various values of Cpk.

## Directivity (active directivity)

Defined as the difference between isolation and forward gain in dB. It is an indication of the isolation of the source from the load, or how much the load impedance affects the input impedance and the source impedance affects the output impedance. The higher the active directivity (in dB), the better the isolation.

## Dynamic range

The power range over which an amplifier provides useful linear operation, with the lower limit dependent on the noise figure and the upper level a function of the 1 dB compression point.

**Gain flatness**

Indicates the variation of an amplifier’s gain characteristic over the full frequency response range at a given temperature expressed in ±dB. The value is obtained by taking the difference between maximum and minimum gain, and dividing it by two.

## Gain (forward gain, G)

The ratio of output power to input power, for RF amplifiers, specified in the small-signal linear gain region, with a signal applied at the input. Gain in dB is defined as G (dB) = 10 log_{10}G.

## Harmonic distortion

Produced by non-linearity in the amplifier, and appears in the form of output signal frequencies at integral multiples of the input signal frequency. Because harmonic distortion is influenced by input power level it is generally specified in terms of the relative level for the harmonics to the fundamental signal power.

## Isolation

The ratio of the power applied to the output of the amplifier to the resulting power measured at the input of the amplifier.

## Linearity

Signifies how well an amplifier’s output power can be represented by a linear function of the input power. A linear amplifier produces at its output an amplified replica of the input signal with negligible generation of harmonic or intermodulation distortion.

## Maximum signal level

Refers to the largest CW or pulse RF signal that can be safely applied to an amplifier’s input. Exceeding the specified limit can result in permanent noise figure degradation, increased distortion, gain reduction, and/or amplifier burnout.

## Noise factor

The ratio of signal-to-noise power ratio at an amplifier’s input to the signal-to-noise power ratio at the output. Noise figure NF in dB is related to noise factor F by NF = 10 log_{10}F in dB.

## Return loss (RL)

The ratio of reflected power to incident power at an RF port of an amplifier, expressed in dB as RL = -20 log |ρ|, where ρ = voltage reflection coefficient.

## Reverse gain

The ratio of power measured at the input of an amplifier to the applied power at the output of an amplifier, also known as isolation.

**Sigma**

The statistical term for the standard deviation of a distribution. All nominally identical things differ one from another to a greater or lesser degree. Standard deviation is a measure of how much a distribution varies around the average (mean) value. Many distributions when plotted have a bell-shaped appearance, and are characterized as a normal distribution.

The standard deviation is the distance from the center of a normal distribution curve to where the curve changes direction (its point of inflection), and is denoted by the Greek letter sigma (σ).

**Sigma performance,**

SP, tells how far the nearest spec limit is from the average, compared with the sigma value. For example, if the spec limit is six sigma away, the process has SP = 6. Thus, SP equals three times the Cpk value.

## “Skinny” sigma

Refers to a process having small standard deviation and process width (the width at ± 3σ) relative to the specification limits. It reflects a favorable relationship between the process width and the width of the specification. For example, in a well controlled process the deviation from one unit to the next is small, and most units fall well within the spec limits. Narrow variation indicates “skinny” sigma. In a process that is not tightly controlled, units will vary from one spec extreme to the other or even exceed the spec limits; in that case the process width and sigma are wide. What causes some confusion is the fact that six sigma is skinny while two sigma is wide; six sigma means the spec limits are much further away from the distribution.

## Stability

An indication of how immune an amplifier is to self-oscillation, so that it does not generate a signal at its output without an applied input. A commonly used indicator of stability is the k-factor. A k-factor of 1.0 is the boundary condition for unconditional stability. If it is greater than zero but less than 1.0 the amplifier is only conditionally stable.

## Two-tone third-order intercept point

A measure of third-order products generated by two equal-amplitude signals arriving simultaneously at the input of a device such as an amplifier. If F1 and F2 are the frequencies of the two signals arriving at the input, the amplifier generates intermodulation products at its output due to inherent non-linearity, in the form ± m × F1 ± n × F2 where m and n are positive integers which can assume any value from 1 to infinity. The order of the intermodulation product is defined as m + n. Thus, for example, 2 × F1 – F2, 2 × F2 – F1, 3 × F1 and 3 × F2 are third-order products by definition. The first two products are called two-tone third-order products as they are generated when two tones are applied simultaneously at the input. The latter two are single-tone third-order products, usually called third-harmonic products.

For example, if 100 and 101 MHz are the frequencies of two applied signals, then 99 and 102 MHz are the two-tone third-order products and 300 and 303 MHz are singletone third-order products. Two-tone third-order products are very close to the desired signals and are very difficult to filter out. Hence they are of great importance in system design. In the linear region, third-order products decrease/increase by 3 dB for every 1 dB decrease/increase of input power, while the desired output signal power decreases/increases by 1 dB for every dB of input power.

When drawn on an X-Y graph with input power on the X-axis and output power on the Y-axis, third-order products fall on a straight line with a slope of three, while the desired (fundamental) signal power falls on a straight line with a slope of one as shown below. By extending the linear portions the two lines, they intercept at a point. The X co-ordinate and the Y co-ordinate of this point are called the input and output third-order intercept point respectively, and the two differ by an amount equal to the small-signal gain of the amplifier. In the example shown, small-signal gain is 30 dB and output IP3 is 40 dBm.

Output intercept point, IP3 (dBm)out, can be calculated using a simple formula:

IP3 (dBm)out = Pout (dBm) + A/2

Where Pout (dBm) is the output power of each tone in dBm and “A” is the dB difference between the per-tone output power and the intermodulation power. Input intercept point is obtained by substituting Pin (dBm) for Pout (dBm) in the above formula. Single-tone and two-tone third-order intercept points differ by a fixed amount on the Y-axis, but the output/input lines have the same slope.

## Unconditionally stable

Refers to an amplifier that will not oscillate regardless of load or source impedance.

## VSWR

(Voltage standing wave ratio) is related to return loss (RL) by the following:

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