amateur service newsletter W6SAI Intermodulation Distortion Although there has been much talk about intermodulation distortion ia in Linear Amplifiers linear amplifiers, a search of avail- able literature brings to light very little in the way of factual data. Here's down-to-earth dope on what BY WILLIAM I. ORR.* W6SAI linear-amplifier tubes can and can't do. T is common communication practice to gen- tones (or frequencies) and as the perfect linear erate a single-sideband signal at a low power amplifier has yet to be built, the situation leading I level for reasons of economy and then to am- to IM distortion exists in most 8.s.b. amplifiers. pilfy it to the desired strength by the use ol one Once the intelligence-bearing signal has been gen- or more linear amplifier stages. The intelligence erated, the amplitude relationships existing in the is contained in amplitude variations in the signal, intelligence must be faithfully retained or the and it is imperative that the linear stages amplify s.s.b. signal will blossom into a broad, fuzzy this intelligence with as little distortion as possi- caricature of itself, and the unlucky user of the ble. Strictly speaking, an ideal linear amplifier nonlinear equipment will find his on-the-air is one in which the output envelope amplitude is popularity waning. Intermodulation distortion, at all times directly proportional to the input therefore, is important to the 8.s.h. operator, and envelope amplitude. Amplitude distortion results the cause and effect of this unloved and unwanted when the magnitude of the output signal is not mutilation of s.s.b. signals will be discussed in strictly proportional to that of the driving signal. this article. This class of dist.ortion (which is the principal type encountered in linear amplifiers) includes The Vacuum Tube and Linearity intermodulation distortion, a particularly interest The vacuum tube is the heart of the linear ing type of amplitude distortion encountered in amplifier, and the amplifier is designed ahout it.' single-sideband service. In passing, it should be In addition to the tube, the amplifier is composed noted that intermodulation distortion (abbrevi- of auxiliary eqdipment - resistors, capacitors, ated IMD) occurs only in a nonlinear device inductors, etc. - chosen to permit the tube to driven by a complex signal having more than one operate in the most linear manner possible con- frequency. As speech is made up of multiple sistent with various restrictions imposed by eco- * Amateur Service Department. Eitel-hlcCullough, Inc., nomic, physical and electrical limitations. The San Carlos, California. auxiliary equipment may be considered to be made up of passive circuit elements while the vacuum tube is thought of as an active element by means of which the desired power gain is accomplished. The passive circuit elements are entirely linear and they affect circuit operation only insofar as they determine the operating parameters of the tube. The linearity of the tube is open to question. The more linear the tube, the less stringent the demand placed upon the cir- cuitry to achieve a desired degree of over-all linearity. The results obtained are a balance between excellence and economy. The vacuum tube utilizes electrons emitted from a hot cathode by impressing upon them an electric field which varies with time. During the paasage of the electrons from cathode to plate, the field is manipulated in such a way as to alter the number of electrons arriving at the plate of the tube. The electric field reacts in a predictable way that may be accurately described by Max- EQUIVALENT PLATE VOLTAGE well's equations. The electron flow (or cathode Fig. 1 -The electron flow (cathode current) in a vacuum current) is a 3/2 power function of the appl~ed tube is a nonlinear function of the equivalent plate (or plate electrode voltages. This so-called "3/2-power and screen) voltage and is described by the 3/2-power 1 Th~sd~scusa~on appl~es to vacuum tubes S~mllarconclu- law. This curve illustrates typical electron flow, which plays slons may be drawn about trans~stors,but such conclusions an important part in establishment of tube linearity. are not wlthin the scope of this article. law" of Child and Lnngmuir is theoretically valid for uniform tube geometry and holds true for any space-charge-limited electron flow under the influence of an external field (Fig. 1). The 3/2- power law is not a linear function, and in practical tubes the cathode current is not a straight-line function of grid voltage. Further, practical tubrs depart from the 3/2-power law to some extent, drprnding upon tube geometry, space charge, elrctron intrrcrption by grids, and emission limitations. Thr relationship between the electric field and cathode-current flow within the tube described hy this natural law plays an important role in the establishment of tube linearity. In practical amplifiers, for example, the magnitude relation- PEAK AMPLIFIER DRIVING VOLTAGE - ship between input and output signals is not Fig. 2-Amplifier linearity is defined by the envelope perfrctly constant at all signal levels within a transfer function. Departure from linearity is illustrated by given range. The relationship defining ampli$er curvature of the function (dotted curve) and may be traced linearity is termed the envelope transfer function, directly to the nonlinear relationship between cathode and ideal and typical transfer functions are current and electrode voltage shown in Fig. 1. shown in Fig. 2. The fundamental cause of a non-idpal, nonlinear amplifier transfer function tion determining the excellence (or lack thereof) mav be traced directly to the nonlinear relation- of linear amplifiers and tubes. ship between the plate current and grid voltage A practical test technique is to employ a two- of the tube employed in the amplifier. This rela- tone, low-distortion test signal to drive a linear tionship approzimates the 3/2-power law through- amplifier, and to use a spectrum analyzer to dis- out the operating reglon above cutoff.2 An exam- play a sample of the output signal of the amplifier ination of intermodulation distortion reveals the (Fig. 3). A spectrum analyzer is a precision pano- importance of significant cathode-current de- ramic receiver having high resolution and capable parture from this fundamental law as regards of resolving signals separated in frequency by amplifier linearity. only a few kilocycles. The presentation of a por- tion of the spectrum in which the tests are taking Intermodulation Distortion Measurement place is given on a long-persistence cathode-ray Techniques tube. If the IMD products of the two-tone test Leaving the vaculim tube for a moment, it is signal are known and the amplifier under test is useful to examine means of testing tuned linear run with no feedback, at a frequency low enough amplifiers for distortion. One such means is to to remove side effects due to circuit uncertainties, apply two equal-amplitude r.f. signals of different the IMD products of the tube under test may be frequency to the input circuit and then to meas- readily determined by visual inspection of the ure the relative strengths of the output signals picture on the screen of the spectrum analyzer. and the accompanying intermodulation prod- Equally important is the fact that the test is re- ucta? This combination of input signals is often producible, and that the tube may be operated called a two-lone test signal. The action of the test under any combination of electrode voltages and signals beating with each other in the typical loads. "nonlinear" linear amplifier having amplitude A block diagram of a typical IMD test ex- distortion produces intermodulation distortion, periment is shown in Fig. 4. The low-distortion and the purpose of the two-tone test is t.o create signals are generated by eeparate stable r.f. oscil- this action under controlled conditions and to lators operating on 2000 and 2002 kc., respective- measure it. Maximum limits of intermodulation ly, their outputs being carefully combined in a di~t~ortionhave become an important specifica- special isolator which prevents the oscillators Cutoff may be thought of as that amount of grid bias requid to reduce the idl~ngplate current of a vacuum tube to virtually zero. "The Grounded Grld Linear Amplifier." Orr. Rinaudo. Sutherland: QST. August. 1961, pages 16-21. Fig. 3-QST authors and prominent DXers W6KEV (stand- ing) and W6UOV examine data plotted by Eimac Inter- modulation Distortion Analyzer. General-purpose equip- ment permits IMD measurements to be mode on a wide variety of transmitting tubes in either grid- or cathode- driven configuration. IMD products are seen on screen of panoramic analyzer. TWO -TONE TEST GENERATOR r--- - - --- - - -- ---- - - ----"' 1 1 I Fig. 4-Block diagram of Inter- I modulation Distortion Analyzer of I TEST I AMPLFIER Fig. 3. Low distortion two-tone r.f. signal is generated at 2 Mc and POWER applied to test omplifier. The out- SUPPLIEs put of the amplifier is dissipated in a dummy load and o portion of the output signal is examined on the screen of a high resolution pono- 1 2002 KC ramic analyzer. Distortion products as low as -60 decibels below peak power may be seen - - I I and studied. from "seeing" each other. The resultant two- impressed upor, the tube at the convenience of the tone sign:~l is amplified by successive class A operator. The output of the test amplifier is dis- stages until the desired driving level is reached. sipated in a dummy load and a small portion of The two-tone generator shown in the photograph the output signal is applied Lo a panoramic an- is capat)lc of dcslivering a test signal having IMD alyzer having a dynamic range of 60 decibels.