DISTORTION

Any deviation from the original signal waveform is called distortion.These are mainly two types of distortion.

• Nonlinear distortion.• Frequency distortionNon-linear Distortion• If an active device or circuit has nonlinear characteristics then the

output contains new frequencies which are not present in the input signal. The current in the system is given by a nonlinear function.

• i = avi +abj2 +CVI 3

• If vi = A sinωt, the current contains the harmonicsFrequency Distortion• Frequency distortion occur when the gain magnitude i.e., the response

of the system is subjected to frequency distortion. When the signal contains different frequencies, each frequency is amplified differently with consequent distortion of the waveform.

An amplifier with poor high frequency response distorts an input square wave into

poor low frequency response

Phase DistortionPhase distortion is a result of unequal phase shift of signals of different frequencies. This distortion is due to the fact that the phase angle of the complex transfer function of a system depends on frequency.Intermodulation distortionMany signals to be amplified or processed are not sinusoidal. They are a composite of many frequencies. In a linear system there would be inter action of these frequencies. In a nonlinear circuit, signals of different frequencies will inter-modulate to produce sum and difference frequencies. The distortion of signal takes place because of the non-linear characteristics of amplifier circuit elements like transistors. This distortion is called the harmonic distortion.

Harmonic DistrotionHarmonic distortion is measured by the ratio of the amplitude of a particular harmonic to that of the fundamental.If B1, B2, B3 ------------ Bn are the amplitude of the first, second, third and n th harmonics present in a waveform.

The total harmonic distortion or distortion factor is given by.

There are different methods available for determining harmonic distortion in a waveform.

So total harmonic distortion,

The amplitudes and frequencies of these harmonics can be determined by Fourier theory.Fourier theory states that any periodic waveform is equal to the sum of a dc term plus sum of series of harmonically related sinusoids.

Tuned Circuit Harmonic Distortion Analyzer

Functional block diagram of tuned circuit harmonic analyzer

In this technique a series resonant circuit is subjected to the waveform to be analyzed and the voltage developed at that frequency is amplified, detected and measured using a meter.The series resonant circuit is tuned to different harmonics, and their relative amplitudes are noted.

LIMITATION:The a.c resistance of the series resonant circuit and the gain of the amplifier will vary with frequency. To compensate for these variations, a parallel resonant circuit is connected across the input terminals.

There are certain limitations associated with this simple technique.

• At low frequency large value of L and C are required. Due to their physical size and consequent losses make their use impractical.

• Higher harmonics of the signal are often too close to each other. It is difficult to distinguish between them. So the output what ever we get is the total harmonic distortion.

Heterodyne Harmonic Analyzer

The input signal to be analyzed, after necessary attenuation is mixed with the output of the local oscillator. Each harmonic of the input waveform mixes with a particular frequency of the local oscillator and produces the characteristic frequency of the active filter. Thus each harmonic is converted to a constant frequency. This frequency is passed on to the meter amplifier and detectorby a highly selective filter of the quartz crystal type.

The mixing circuit used in this techniques is a balanced modulator which successfully eliminates the first harmonic of the original signal. In addition the balanced modulator generates very low harmonic distortion.

The meter may be calibrated directly in terms of voltage or amplitudes of different harmonics may be compared with a reference voltage. Usually amplitude of different harmonics are compared with the fundamental.

In direct reading analyzers a low pass filter allows only the difference frequency which is called as frequency selective voltmeters. This voltage is compared with the input signal and read off on a calibrated voltmeter in db.

Heterodyne Harmonic AnalyzerThe heterodyne harmonic analyzer shown in previous slide over comes the limitation of the tuned circuit harmonic analyzer.

AMPLIFIER

Fundamental-Suppression Distortion AnalyzerHarmonic distortion analyzers are based on the fundamental suppression which are employing

• A resonance bridge.• Wien bridge method.• Bridge T - network method.

Harmonic distortion analyzer measure the total harmonic power present in the test wave rather than the distortion caused by each component.

BridgeAmplifier

With short between AB, ET

Total harmonics are measured.Without short, only total harmonics EH are measured.

1. The input signal is fed to the 1MΩ input impedance 50db attenuator, 10db step, which is controlled by a switch marked sensitivity situated on the front panel.

2. The signal is fed to the impedance converter which is a low distortion, high input impedance unity gain amplifier.

3. Then the signal passes through the rejection amplifier system. It consist of a preamplifier with a Wien bridge tuned to the fundamental frequency, and a bridge amplifier. The Wien bridge couples the preamplifiers and the bridge amplifier.

It suppresses the fundamental frequency and allow all other harmonics.

4. The output of the bridge amplifier is connected to the meter circuit via a post attenuator. The post attenuator limits the signal level to 1mv for full scale deflection. It is a low drift, low noise one with flat response. The meter scale is calibrated to RMS values of sine wave.

Negative feedback between the bridge amplifier and the pre-amplifier sharpens the response-of the Wien bridge there by enhancing selectivity of the system.

To measure total harmonic distortion point A and B are shorted. Then the meter reads ET , the total of the fundamentals and harmonics. Now the short between A and B is removed and the meter reading EH gives a measure of the harmonics. The total harmonic distortion is then given by

FREQUENCY SPECTRUM OF WAVEFORM

The frequency composition of a signal, as expressed by the Fourier Series, is called the frequency spectrum of a signal. Such a frequency spectrum of a waveform can be plotted on a graph, with the frequencies of harmonics on the abscissa (X-axis) and their amplitudes on the ordinate (Y-axis).Let us consider again an ideal sawtooth waveform. With the help of mathematicalA calculations, it can be determined that the amplitude of n.th harmonic is equal to A/n where A is the amplitude of the sawtooth waveform. So amplitude of first harmonic is equal A/, amplitude of 2nd harmonic is equal to A/2, and so on. Frequency spectrum of the saw tooth waveform is shown in Fig. 24.3.Different waveforms have different frequency spectrums. Frequency spectrum of any waveform gives: (i)what are the harmonics present in the waveform, and (ii)The amplitude of the harmonics present.

From Fig. 24.3 it can be seen that all harmonics are present and amplitude of higher harmonics approach zero.

Spectrum Analyzer.

Display of frequency spectrum on the screen is very helpful in the analysis of any input signal because it gives the information about location and strength of all the frequency components of the input signal.Spectrum analyzers use either a parallel filter bank or a swept frequency technique.

Fig. Spectrum Analyzer (Parallel Filter Bank Analyzer)

Typically an audio-analyzer will have 32 of these filters, each covering one-third of an octave.For wideband narrow resolution analysis, particularly at RF or microwave signals, the swept frequency technique is preferred.Spectrum analysis is divided into two major categories on account of instrumentation limitations and capabilities. These are • Audio-frequency (AF) analysis.• Radio-frequency (RF) spectrum analysis. The RF spectrum analysis covers a frequency range of 10 MHz to 40 GHz, and is, therefore, more important as it includes the vast majority of communication, navigation, radar and industrial instrumentation frequency bands.

• Frequency of a tunable oscillator is linearly swept electronically and filter output is supplied to the vertical deflection plates of a CRO.

• As the oscillator frequency sweeps, amplitude of frequency components appear on the screen one by one, separated from each other in horizontal direction.

• Separation of display of various frequency components on the screen is made by supplying a sawtooth wave signal to the horizontal deflection plates of the CRO. The same sawtooth wave signal is supplied to the oscillator to sweep it.

Sweep is done at a rapid rate so that the display of the frequency spectrum appears constant and a real time-picture can be observed on the screen.

Input signal is passed through an adjustable attenuator and then mixed in a mixer with the signal from a variable frequency oscillator. This mixed signal is then filtered in the fixed frequency active filter. The output of filter is then detected and supplied to the vertical deflection plates of a CRO. Sawtooth signal generator supplies the signal to the oscillator and the frequency of the oscillator is controlled by the instantaneous value of the sawtooth voltage.The oscillator frequency sweeps linearly and increases from its minimum value to its maximum value as the sawtooth voltage rises from its minimum value to its maximum value. The same sawtooth signal is supplied to the horizontal deflection plates of the CRO. So it can be said that when sawtooth signal starts to rise from its minimum value, two events occur at a time. 1. Frequency of oscillations starts to increase. 2. Spot on the screen starts travelling in horizontal direction.

Block Diagram of a Basic Spectrum Analyzer

VCO

Three-Dimensional Presentation of Amplitude, Frequency and Time

Spectra of Different Signals. Let us now study some of the commonly used signals in order to illustrate the spectra which are displayed on the CRO when they are applied to the spectrum analyzer. Continuous Wave (CW) Signals. When a continuous wave input signal is slowly swept through by a spectrum analyzer's local oscillator, the response displayed on the screen is a plot of the IF amplifier pass band. Since the CW signal has energy at only one frequency, the display on the screen will be a single spike which occurs in case the total RF sweep width or spectrum width is wide as compared to the IF bandwidth in the analyzer.

(ii) Amplitude Modulated (AM) Signals: We know that when a continuous wave (CW) signal of frequency fc is amplitude modulated by an input signal of frequency fs, two side-band frequencies of (fc + fs ) and (fc - fs ) are produced. The display on the screen of spectrum analyzer screen is a signal of frequency fc, with two sideband frequencies whose magnitude relative to the carrier frequency depends upon the percentage of modulation.

A Single Tone AM Display on Analyzer

(iii)Frequency Modulated (FM) Signals:

If a continuous wave (CW) signal of frequency fc is frequency modulated at a rate fr, it will develop an infinite number of sidebands. These are located at intervals of fc = nfr where n is an integer (1, 2, 3,…..). However, in practice, only the side bands containing significant power are usually considered.

Amplitude-Spectrum of Single Tone FM

(iv) Pulse-Modulated Signals: An idealized pulse waveform in time domain is illustrated in Fig. (a), but for the analysis of its frequency spectrum, it must be broken into its individual frequency components, as illustrated in Fig. (b) Green chart.

A spectral plot in the frequency domain has been given in Fig. (a) RED, where the amplitude and phases of an infinite number of harmonics are plotted resulting in a smooth envelope as illustrated in (b).

Pulse Modulation Spectrum

There are many more applications of spectrum analyzer, few of these are given below : (a)Pulse width and repetition rate measurements (b) Tuning a parametric amplifier (c) FM deviation measurements (d) RF interference testing (e)Antenna pattern measurements.