Full version in "Microwave System Design Tools and EW Applications" published by Artech House, Inc.
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Amplifier Dynamic Range

 Introduction

This Applet examines the effect of amplifier compression/limiting characteristics on the intermodulation and dynamic range performance.

The display on the upper left depicts the linear compression characteristic. The scroll bar to the upper left allows the sharpness/slope of the compression to be modified. The corresponding 1dB compression point referred to the input is indicated.

The display on the lower left shows the two-tone frequency spectrum and intermodulation products as a function of input drive level, controlled by the lower left scroll bar and compression slope. As an example, the two tone frequencies chosen are 110MHz and 130MHz. The order of the intermodulation components |m ± n| are indicated

The main display to the right shows the amplifier input/output transfer characteristic on a logarithmic (dB) scale. The amplifier gain is normalised to unity so it is convenient to refer all measurements to the input. Actual system gains and limiting levels can be adjusted accordingly. The display indicates fundamental signal gain and signal levels of 3rd, 5th, and 7th order components as a function of signal level and/or compression sharpness. The intermodulation analysis accuracy sets the upper input power to 0dBm .

Corresponding -1dB compression and 3rd order intercept points are indicated from which, single tone and two-tone dynamic ranges can be calculated. Pmin is set by system factors such as noise level or detection/processing thresholds.

The Save Button saves relevant data to the Java Console. Data may be selected on the Console using the mouse (Shift-click) and copied to the clipboard ( Ctrl C ) and saved in a text file for a permanent record or transferring to Excel for example.

If visual plots are required, Alt-Printscreen, copies the current window to MS Clipboard.

 Background

1) Introduction

Broadband RF amplifiers suffer from intermodulation distortion at high input signal levels due to linearity deviations and saturation effects. At very high levels the amplifier enters a compression or limiting region before burnout becomes a problem. High gain limiting amplifiers are designed to be over driven and the intermodulation performance is easier to calculate. Harmonics of the input signals are only important for octave and greater bandwidth amplifiers. Intermodulation components can cause problems in narrower bandwidth amplifiers.

Amplifiers are usually characterised by the 1dB compression level or the 3rd order intercept point. The latter, if specified, allows the 3rd order intermodulation levels to be predicted as a function of two-tone signal levels. Except for particular cases, there is little relationship between the 1dB and 3rd order intercept levels. The difference is in fact a function of the amplifier compression characteristic as is shown by the applet.

 

2) Amplifier Transfer Characteristic

It is usual to describe the transfer characteristic of an amplifier by a power series of the form,

where, v is the input and Vo the output signal.

In principle, any real characteristic can be approximated by suitable choice of the coefficients of such a series, but if the approximation is to be accurate into saturation then many terms are required.

The first term is a DC component. The second is the linear gain. The third and all even power terms are normally zero for symmetrically saturating amplifiers, but would produce even harmonics and intermodulations of the input signals if unbalanced. The higher power odd terms describe the curvature amplifier characteristic in more and more detail.

 

3) 3rd Order Intercept Point

For two tone input signals,

Usually the dominant intermodulations are the third order terms ( ) and ( ). With sharp compression amplifiers, the higher odd order series terms become more significant but all produce third order intermodulation components which combine or interfere with the dominant 3rd order signal. Similarly for 5th and 7rth This effect can be observed in the applet.

Arising from the cubic power term, the magnitude of the 3rd order components increases as the cube of the input signal. On a log-log plot this shows up as a slope, 3 times faster than that of the the fundamental. As the signal drives the amplifier into saturation, all components become compressed, but if the initial slopes of the fundamental and 3rd order intermods are projected, the point where they intercept is termed the 3rd order intercept. This point is useful as it can be determined practically from a few measurements and from it, the two-tone dynamic range can be estimated for any system once the sensitivity Pmin has been defined.

4) Amplifier Model

The amplifier compression characteristic used in this model is,

where, v and V0 are the input and output signals and the exponent N controls the rate of compression near saturation. The larger the value of N, the sharper the saturation knee.

A power series approximation is developed in the applet, based on Lagrange Interpolation, to simplify extraction of the intermodulation components using the FFT algorithm and extending it's validity over very wide differential signal dynamic ranges.

5) Simplified Intercept/Compression Point Analysis

In the case where, the cubic term in the amplifier power series predominates,we can use just the first two terms of a limiting amplifier voltage transfer characterisic,

(1)

where, vi , vo are the input and output voltages, g is the voltage gain, and V is the 1dB compression point.

let

then each fundamental signal output component is of the form,

At the 1dB compression point, vo /gvi = 0.89 (a = 0.11), and the input signal voltage amplitude is from Equation 1,

(2)

The third order intermod component amplitude (at cos(2 omega 1 - omega 2 )) from substitution in Equation 1 and evaluation is,

(3)

At the 3rd Order Intercept point, b-> b12 and v12 = gb12. Solving this identity, the input signal power is,

(4)

The power ratio between the 3rd order intercept and 1dB compression points from Equations 2 and 4 is,

This value is close to that observed for slope/sharpness values in the mid-range. For most practical amplifiers, it may be possible to use this basic approximation.

6) Simplified Compression Points of Cascaded RF Stages

Taking the first two terms of an amplifier saturating characteristic, we get,

(1)

where, vi , vo are the input and output voltages, and G1 the voltage gain, and V1 is the 1dB compression point.

By cascading two stages, the final voltage at the second stage output is,

(2)

Extracting the first two terms again, this simplifies to,

(3)

Comparing equations 1 and 2 the cascaded compression point V12 is found from,

Once again, for most practical amplifiers, it may be possible to use this basic approximation.

7) Summary

The applet shows the effect of amplifier saturating characteristics on the useful single and two-tone dynamic ranges.

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