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A METHOD OF OBTAINING LINEAR FREQUENCY DEVIATION IN A WIDE-BAND

F R EQU EN C Y - MOD U LA TI ON SY STEM*

By Z. K. MASS, Dipl. Ing.f

(The paper was first received 22n d January, and in revised form 2\st March, iy47.)

SUMMARY

This report describes u method of obtaining linear frequencydeviation in a wide-band frequency-modulation system. The primarycause of harmonic distortion in a frequency-modulation system is thenon-linenrity of the slope of the reactance valve. A method isdescribed of linearizing this slope, and thereby obtaining very goodlinearity of the frequency mo dulation. The harmonic distortion is ofthe order of 60 db below the fundamental.

This report also describes a method of checking high-fidelityfrequency modulation.

(1) CAUSES OF NON-LINEARITY IN F.M. SYSTEMS

The non-linearity of the frequency deviation occurring inoscil lators controlled by any conventional reactance valve, isdue primarily to the non-linearity of the slope, g tn, of the reactancevalve. Th e linearity of the deviation is also a function of thedeviation ratio, so that i t would be impossible to obtain therequ ired linearity with a deviation of ± 100 kc/s on 300 kc/s bydirect means.

Oscillator

A reactor valve connected across an oscillating circuit L0C0,as shown in Fig. 1, may represent either an inductance L r, or acapacitance C r, depending upon the phase-shift network.

(a) When the reactance valve represents a capacitance C r:

1 1 to 0

W'" V f t Q ^ g ) ' V[L0C0(l i CrIC0)] " V

where "° WThe quantity Cr/C0 will be called k, this quantity being very

small compared with unity.,

coQWe have therefore co

into a power series as follows:+

which may be expanded

\){n 2)

273"

Put t ing n equal to

o>0(lco

• •> w e h a v e :

O-5AH-O-375A:2 .)

• Radio Section paper.t British Telecom munications Research , Ltd.; formerly with Signals Research an d

Development Establishment.

The factor 0-5A represents the linear deviation Aco, andthe factors containing higher powers of A represent the distortion.

The frequency deviation is : 0-5/()A, therefore the totaladmissible deviation A /i s equal to f {)k, where 2^ o> {).

(b ) When the reactance valve represents an inductance /.,.:

1Lo

Lr

c

/G/\)I0/L r)

Where

Here again the quantity LQ/l .r is very much less than unity,and may be called k.

(2) LINEARIZATION OF THE SLOPEVALVE

OF A REACTANCE

Assuming that the grid voltage VgU applied to a valve is givenby the function V Xt - e 0 r c'i sin cot, the slope gm of the valvemay be defined in two ways:

(a ) When the grid excitation ex is infinitesimal, then

g ,.__*>..dv

s\t

This may be defined as the differential slope (gj^).(b ) When the grid excitation el is large, the plate current / (;/

may be expressed in the form of a Fourier series:

Iat r - 70 -!- /, sin (cot h sin {2cot i-/ „ s i n (mot •; </>w)

Where <f>y, cf) 2, etc., represent successive phase angles.The ratio Il/e l may be defined as the incremental slope (g incr.)

at the working point defined by e0, and in all practical applica-tions it is this incremental slope with which we are concerned.

A method of correcting the incremental slope of a valve isshown in Figs. 2 and 3. An r.f. voltage [e in Fig. 2(6) of constantand small amplitude, i.e. small in comparison with the cut-offbias] is fed to the control grid, Gj, of the valve, the slope ofwhich is to be corrected. The modulating voltage, Vm, is also

fed into the same grid; this voltage sweeps the whole gm charac-teristic and thus alters periodically the working point of thevalve as shown in Fig. 2(«).

Under these conditions, the r.f. compon ent, frr of the platecurrent appearing in the anode circuit is strictly proportional tothe instantaneous slope gr

Two distinct conditions may be considered.(a) If the r.f. current is rectified and gm is proportional to the

modulating voltage over the range of the valve characteristiccovered by the latter, then the envelope of the rectified currentwill represent the undistorted modulating voltage and nocorrection would result, or would be necessary.

(b ) If gm does not vary proportionately to the modulatingvoltage, then the envelope of the rectified current will representa distorted modulating voltage.

[ 4 9 7 ]

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M A S S : A M E T H O D O F O B T A I N I N G L I N E A R F R E Q U E N C Y D E V I A T I O N I N

'S *in

k • f t

emvbj:

uuUllu

V !h e y r i e —

Fte— ib i L

•^ cycle

- v

rt

H Ivoltage

i H.F. choke

(a) (b)

Fig . 2 . Co r r ec t io n o f in c remen ta l s lo p e (1 ) .

EM.oscillator

H.F linearamplifier

Linearrectifier

Low-passfilter

LinearL.F.

amplifier

Phase-shift-correcting |network

i^. 3.--Correction of incremental slope (2).

A v oltage is therefore obtained which represents the distortionof the modulating voltage due to the variation in gm not beingproportional to the modulating voltage, and this can be fedback into the grid circuit in anti-phase, thus reducing theharmonic distortion due to non-linearity of the slope charac-teristic in accordance with negative feedback theory.

This method of correcting the incremental slope of the reactorvalve in f.m. application gives very low tota l harmo nic distortion:the second and third harmonics may be reduced to 60 db belowthe fundamental level.

Referring to Fig. 4 curve B shows how the slope gm of a("VI73 valve varies with the modulating voltage on the grid,while curve A shows the slope characteristic when correctedin the manner described above.

Referring again to Figs. 2 and 3, the condenser C l shouldoffer sufficient by-pass for the high frequency exciting voltage e,but at the same time should be small enough to avoid shortcircuiting the low-frequency voltage Vm.

Condenser Q , in conjunction with the input condenser (C in-put ) forms a voltage divider, thus reducing the effective high-frequency excitation. When the modulating voltage Vm isapplied, the input capacitance varies (space-charge variation)thus giving additional cross modulation of the exciting voltage,e, by the v oltage Vm. This effect may be reduced to a negligible

12

10

•db

Ay

VyAr

A(A

A

</

00

520

104 0

1560

2080

25100

30B120 A

Fig. 4.—Slope characteristic of CV 173 valve.

order by mak ing A( C inpu O/C , sufficiently small . The factor

A(C input)/C! in a reactor valve will have a detrimental in-fluence on the linearity of the frequency deviation . A suitable

value for C, is usually 100-200 JU/ZF.

(3) LINEARIZATION O F FREQUENCY DEVIATION

Referring to Fig. 3, l inearization of the frequency deviation

of an oscil lator by a reactance valve may be achieved by using

a separate (auxiliary) oscil lator of a frequency of about 60 to

100 Mc/s .

A n alternative circuit using the h.f. oscil lations from the f.m.

oscil lator i tself for l inearization purposes is shown in Fig. 5.

Fig. 5.—Linearization of frequency deviation.

This is superior to the two-valve circuit but requires more carein the design. Th e r.f . curre nt of the reactance valve is tak enthrough the ca thode coi l Lx and the minute vol tage appear ingacross this coil , due to In, is coupled to coil L2 and finallyamplified in a l inear r.f . amplifier (as shown in Fig. 3), havingsufficient bandwidth to make ample allowance for frequencymodula t ion. The amplified voltage is then rectified by a l inearrectifier (a diod e work ing at high level) , the ou tpu t, after filtering,being again am plified in a l ine ar a.f. amplifier which reverses,at the same time, the pha se of the rectified voltag e. A n addi-t ional phase shift network inserted in the negative feedback looprestores the original phase relations.

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A WIDE-BAND FREQUENCY-MODULATION SYSTEM 499

(3.1) Precautions Necessary for Correct Operation of Circuitshown in Fig. 5

(a) The total impedance of the coil 1^ (working as the primaryof a loaded transformer) should be very small in comparison

with the reactance represented by the reactance valve, otherwisethe frequency characteristics will be affected.(/?) The amplitude mo dulation , due to the varying loa d

represented by the reactance valve, should be eliminated. Fig. 6shows the current and voltage vectors in their respective positions.The loading current /3 flowing throu gh the internal resistance ofthe reactance valve may be compensated by the component //,in opposite phase. If this component is too small, still bettercompensation can be obtained by means of the condenser C3passing an additional (out of phase) component, thus obtainingnearly perfect elimination of the amplitude modulation.

(c) Tn addition to the useful current Irt in coil L l t anothercurrent I2 flows through the same coil, due to the fact that thiscoil lies in the pat h of the r.f. phase-shift ne twork . This un-wanted current must therefore be compensated by a current Tx

(controlled by the adjustable resistor R 2, Fig. 5).When <he above conditions are satisfied, the voltage U (Fig. 5)

will be negligible when the reactance valve is shut, and theopening of the reactance valve will cause the voltage U to riseproportionately to the instantaneous slope.

lrt

kc/s

10200

10100

10000

9900

9800

Fig. 6.— Vectors in linearizing circuit.

(3.2) Practical Details and Results

Practical details of the circuit shown in Figs. 3 and 5 are asfollows:—

Reactance valve—CV173R. F. amplifier—One CV173 with highly damp ed input an d

output circuits.

Diode rectifier—ConventionalA . F . amplifier— One 6V6 cathode follower.

Fig. 7 shows the frequency deviation obtained with this circuitusing three different samples of CV173 (top, middle and bottom).*The graphs demo nstrate the smallness of the frequency shiftcaused by chang ing the reactanc e valve. Once the circuit hasbeen properly set up, i t does not require any additional trimming ,and the neutralization is not affected by changing the reactancevalve. Trim min g of the r.f. amplifier and setting of the neu-tralization can be observed on a meter reading the diode current.

• The d.c. component in the negative-feedback loo p is preserved.

J

cv

o

+

173

Vdl\ e l

3

3 4 5 6 7 8 S 10y

Fig. 7 .—Frequency deviat ion with different samples of CV173 valve.

(3.3) Practical Applications

The ideas and principles described in this paper were appliedin the design of the new 1 — 4 modulator for the Army SetNo. 10 (see Fig. 8).

••1

6

5

8lOMc/s

OJSC.

4

3

35Mc/jsosc. I

10

11

Sender R.F. receiver

Senderpulger

300±100-kc/samplifier

Amplifierand f>licer

Receiverp u l g e r

+ tMixer

Low-paf>5fi l terTOkc/p

103±01-Mc/5oscillator

1

tReactor

+35-MC/S

amplif ier

Ou tpu tamplif ier

300-16000 c/s

Line amplifier300-16000 C/S

>

tDiode rectifierAudio amplifier300- loOOOC/S

13

14

15

16

17

Out

In

XI

Fig. 8.—Block schematic of 1 4 modulator.

As the modu lator had to be suitable for w orking in conjunctionwith the same sender as the Signalling Equipment No. 10, itwas necessary to use pulse modulation with about the same dutyfactor, i.e. about 0-5, and in order to obtain the high degree oflinearity required, it was decided to use pulse frequencymodulation.

A block diagram of the modulator is given in Fig. 8. Theinput from the 1 + 4 line (4-wire system) is amplified in theline amplifier 1, and passed to the reactor 2, which controlsthe frequency of the 10-3-Mc/s oscillator 3. The output from

this oscillator, and the output from a fixed 10-Mc/s oscillator 8,are fed to the mixer 4.

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500 HASS: A METHOD OF OBTAINING LINEAR FREQUENCY DEVIATION IN

The ou tput of the mixer, 300 kc/s modulated ± 100 kc/s, ispassed through the video amplifier 5 to the counting circuit 6.This produces pulses of fixed width at a recurrence frequency of300 kc/s modulated t 100 kc/s by the input from the line, andthese are used to modulate the sender 7.

The video output from the receiver 13 is passed through thevideo amplifier and slicer 14, the receiver pulser 15, the low-pass filter 16, and outpu t amplifier 17 to the 1 ~|- 4 line.

The above is a description of the fundamental principles of themodulator, but in order to obtain the required low level ofharmonic distortion it was necessary to develop a suitablecounting circuit and a means of obtaining linear frequencydeviation. ,

(3.4) Characteristics and Applications of the Circuit

The circuit described above for obtaining linear frequencymodulation possesses all the features of a negative-feedbackamplifier, and has the following desirable characteristics:—

(a) Very good linearity with a large frequency deviation

(e.g. I 200 kc/s deviation in a 10-Mc/s oscillator).(b ) Frequency deviation and centre frequency are independentof valve characteristics, thu s allowing complete interchangeabilityof reactance valves.

(c) Reduction of hum to a greater extent than in a balancedreactor.

The system also gives, as a by-product, very linear amplitudemodu lation. This amplitude modulation is obtained by drivingthe grid of the valve by a constant r.f. voltage and varying thegrid bias in the usual manner with the modulating voltage.When the slope of the valve is corrected by the method described,the r.f. component appearing in the anode circuit is linearlyamplitude modulated.

(4) LINEAR COUNTING CIRCUITThe linearity of the frequency deviation obtained may be

checked by means of the counting circuit, giving a d.c. outputproportional to the frequency.

The conventional type of pulse counting circuit, comprising apulse lengthener relying on a time-constant (CR), is sufficientlylinear with frequency when the mark/space ratio (duty factor) issmall. In the case now under discussion, the duty factor wasabout 0-5, and the counting circuit which was developed, and isdescribed below, conserves very good linearity even to the pointwhen the lengthened pulses are almost touching each other.

The counting circuit chain is shown in Fig. 9 and consists ofthree distinct circuits:—

(i) Pulser.(ii) Artiiicial delay line,

(iii) Triggered pulse lengthener.

The principle of this counting circuit is as follows. Analternating voltage of a given frequency f0, and of arbitraryshape It ••• cf)(t), (sine wave, distorted sine-wave or pulses) istransformed in the pulser circuit A [Fig. 9(a)] into a train of verynarrow pulses having a frequency fx. The two frequencies fQ

and/j are correlated:—

m • i

J\ ./<)» where /;/ and n are integers

An artificial delay line B is connected across the outputterminals of the pulser, thus echoing the narrow pulses. As aresult of the action of A and B, the original train of narrowpulses is followed by a similar train of pulses, slightly delayed intime. Fig. 9(Z>) shows the voltages across terminals 1 and 2,

3 and 4, and 7 and 8.The two trains of narro w pulses trigger the lengthening circuitC, shown in Fig. 10. As a result of this trigger action, the

Fig. 9.—Counting circuit.

lengthened pulses are very well defined (constant length and verygood shape), so that a d.c. component can be obtained fromthe lengthening circuit which is strictly proportional to thefrequency f0. The circuit therefore gives very good linearitywhen used as a discriminator for f.m. signals. Other possible

applications of the circuit are for frequency meters, or forgenerating square pulses of constant width in pulse communi-cation systems.

(5) HARMONIC DISTORTION IN COUNTING CIRCUITSUSED AS DEMODULATORS FOR F.M. SYSTEMS

A train of f.m. pulses of constant width possesses a strongaudio component, and if such a train of pulses is passed throu gha condenser into a limiting amplifier, the variation of the audiocomponent with frequency, due to insufficient by-pass, causesan appreciable change of the pulse shape. This change of shapeproduces, after amplification, serious harmonic distortion.

When condenser feed is used, the linearity of the countingcircuit depends greatly on the value of the capacitors, the valuerequired depending upon the number of limiting amplifier stagesconnected in cascade. At low modulating frequencies the sizeof the condensers becomes prohibitive, and it is therefore pre-ferable not to use condenser feed, but to preserve the d.c. com-ponent througho ut the whole equipment. In a limiting amplifier,the problem of linearity is still more complicated by the variationof grid and screen potentials, as these are often derived from highresistance poten tiome ters. To illustrate the effect of the con-denser feed, let us calculate the plate d.c. component (Idc inFig. 11) in a limiting amplifier, as a function of the recurrencefrequency frec; this calculation will also be valid for very lowmod ulating frequencies / . Fo r further simplification, let usconsider a linear anode-bend detector, biassed just to cut-off.

Positively-going pulses applied to the grid through a condenserwill reproduce similarly shaped (but negatively-going) pijlses inthe anode circuit of the detector. The voltage applied to thegrid is measured in respect to the zero line.

If we assume that the d.c. component is stopped by the con-

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A WIDE-BAND FREQUENCY-MODULATION SYSTEM 501

All valvesEF50

G2andG3;Somitted on drg.

UiFig. 10.—Circuit diagram and waveforms of the counting circuit.

denser feed, so that Sa — Sb in Fig. 11, the para mete r Z may be

calculated f rom the equat ions

and

from which

H ' '

/ /(L S)

Now i/r - / „ , .Eliminating Z from the expression for Sa, we have, when H

equals unity:S a - (L - 5) - K L - % c > + S(L - SW&.

When th e pulses are no t sliced, i.e. when there is no to p limita-tion, H -- Z <; P, H --= 1, S and P are fractional, the d.c. com-ponent.

T

(L (1)

When the pulses are sliced at the level P, so that H Z > P,the cross-hatched area Sc is given by

S.. LP

2SP(L S)

an d - S)f?ec, (2)

When the pulse shape approaches a rectangle, S approacheszero and equations (1) and (2) can be reduced to

*d c ' *-Jre ^ Jrcc.

and'dc

LP frec .

(3)

(4)

Equa tion (3) contains a non-linear factor L2frlc, whereas

equation (4) does not, so that slicing of the pulses is imperativeto obtain good linearity. The non-linear factor, 2SP(L S)f?vc

in equation (2) may be greatly reduced by making L muchgreater than S, or by choosing a low working frequency frec

By preserving the d.c. component, perfect linearity may beachieved for all modulating frequencies.

r

Fig. 11.-—Distortion in counting circuit.(6) REFORMING THE PULSES ON THE RECEIVER SIDE

It is known that in pulse frequency modulation a substantialincrease of signal/noise ratio can be effected by reforming thepulses on the receiver side. When this is done, the input tothe counting circuit will consist of pulses of constant width andheight, and the random variation of pulse width caused by noisewill be avoided. Reforming the pulses in this manner alsogreatly reduces the crosstalk (caused by overlapping of the pulses)in carrier-telephony a pplications. This is due to the fact thatthe counting circuit, described previously, is not affected by theshape of the counted pulses, and therefore its indications areonly a function of the frequency of the pulses.

As an example, the addition of the pulse reforming circuit to

the Wireless Set No . 10 when used with the 1 + 4 m odulatorprovides an average gain in signal to noise ratio and signal tocrosstalk ratio of abo ut 30 db.

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502 HASS: METHOD OF OBTAINING LINEAR FREQUENCY DEVIATION IN WIDEBAND FREQUENCY-MODULATION SYSTEM

(7) PERFORMANCE OF THE COMPLETE MODULATOR

Measurements of harmonic distortion have been carried outwith a complete modulator, details of which were as follows:

(a ) Frequency modulating and linearizing circuit as shown inFig. 8.Main oscillators—100 Mc/s and 10-3 Mc/s.Auxiliary oscillator—approximately 35 Mc/s.Frequency deviation—— lOOkc/s.

(/>) Counting circuit as shown in Fig. 9.Main recurrence frequency—300 kc/s.Recurrence frequency deviation— •: 100 kc/s .Pulse length—1 • 6 microseconds.

(<•) D.C. component preserved, and pulses sliced (limited).

The best results obtained with this circuit were as follows:—

Second harmonic—55 db below the fundamental.Third harmonic 60 db below the fundamental.

High-order harmonics—greater than 80 db below thefundamental.

The figures quoted in (c) above apply to both the 1 H- 4modulator itself and to the overall performance of the whole

link (i.e. including the radio circuits and pulse-reformingcircuits).

Direct measurements of crosstalk were also carried out withthe modu lator used in conjunction with the A.C.T. 1 + 4 lineequipment, and this was found to be 65 db down on any of thecarrier channels when the other channels were modulated byspeech. This result is comparab le with the crosstalk introducedby the A.C.T. 1 -f 4 equipment itself.

(8) ACKNOWLEDGMENTS

Acknowledgments are due to the Chief Scientist, the Ministryof Supply, for permission to publish the paper, and to Messrs.W. Palmer, E. Coop and V. A. G. Brown for considerable helpin its preparation.