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surface1  or   over   the   equivalent   end   aperture planes, 2

essentially contain  the   dominant term

Uy(K-cos6)\

kL(K-cosQ)

where K  — /.0[/.g, k = —

and  ?.g is  the rod  wavelength.   At  frequencies outside the stop-

tsM

Fig. 1A  Composite rod structure

-2 0

Fig.  IB  Radiation patterns at gigahertz frequencies

band,  it  might   be   expected that   the   difference between   theuniform-rod   and   composite-rod patterns could   be  explainedby  the  different dispersion relationships  of the two structures.However, since the mean relative permittivity  of the compositerod   is  less than that  of the uniform   rod,  this indicates that  Kwill be  smaller  for the composite rod. This was confirmed  bymeasurements which gave  a  value  K = 1-22 for  the compositerod compared  to K = 1-33 for the   uniform   rod at   9-4 GHz.The radiation-pattern equations indicate that   the  beamwidthof  the   composite should   be   greater than   the   uniform-rodbeamwidth. This is  seen  to be the  case  at   frequencies belowthe stopband, but the  opposite   is   true   for  frequencies above

the stopband.  The  equation suggests that   the   angular posi-tions of the  sidelobes should   lie  closer   to the  main beam  forthe uniform   rod   than   for the  composite   rod, and   this  wasfound   to be the  case.   The   equation also indicates that   thefirst sidelobe levels should   be   approximately 4-6 dB greaterfor the uniform rod,  and  this is found   to  be the case above  thestopband,  but   appears   to be   somewhat less below   the  stop-band. Since   the   increased gain property   of a   compositestructure is not a  surface-wave-propagation effect, an explana-tion  in  terms  of   the modifying influence   of the rod   structureson   the   direct radiation from   the   feed waveguide 3-4  appearsto  be  more likely.

J. R. BLAKEY 5th February 1973

Microwave Physics Group  epartment of PhysicsUniversity of SurreyGuildford,  Surrey, England

References

1   KEILY, D. c :   Progress  in  dielectrics , (Heyw ood, 1961), 3, pp.  1—452   JAMES,  j . R. :  Theoretical investigation   of   cylindrical dielectric   rod

antennas , Proc. IEE, 196/, 114, (3), pp. 309-3193   BLAKEY,  j . R. :  Calculation   of   dielectric-aerial-radiation patterns ,

Electron. Lett.,  1968,4, pp. 46-474   ANDERSEN, j .  B.: Metallic   and   dielectric aerials . Polyteknisk Forlag ,

Lyngby, 1971

uniform rodcomposite rod

8-5 9-0   9 5

frequencyjGHz

1 0 0

Fig.  2  Beamwidth and sidelobe levels against  frequency  forboth rods  uniform rod/  composite rod

ELECTRONICS  LETTERS 22nd March 1973 Vol.9 No. 

PRECISION DIFFERENTIAL VOLTAGE-

CURRENT CONVERTOR

Indexing terms: Magnitude convertors, Integrated circuits,Differential amplifiers

A   new   differential voltage-current conv enor   is   proposed,which achieves high linearity  and is   substantially temperatureindependent.  The   effects   of   transistor mismatches   and oflimited current gain   are   analysed. Experim ental results   aregiven which show   a   considerable improvement over previouscircuits.

In m any integrated circuits, for example multipliers, 1 the  first

stage  is a   differential voltage-current convertor, consisting  of

a simple differential pair with a   feedback resistor RE betweenthe emitters.This circuit gives satisfactory performances only   if the

resistance  RE is   large compared with   the  dynamic resistanceof  the   transistors; otherwise   the   overall transconductance  ofthe circuit  is   strongly temperature dependent   and   essentiallynonlinear.   On the   other hand,   a   high value  of RE  increasesthe noise,  and   this again limits   the   dynamic range.   Thecircuit proposed (Fig. l a)  performs   a   precision low-distortionvoltage-current conversion, even with   low values  of RE, thusimproving  the  dynamic range.

Consider  the sum of the   voltages around   the   loop  com-prising   the   signal generator,   the   base-emitter voltages   ofTr l s  Tr 4, Tr2 and Tr3 and the   feedback resistor  RE:

v ~VBEl- VBEt -  iRE+  VBE + VBE 3  =  0

Eqn.  1 can  also  be  written   as   follows:

(1)

v-iRE +,  £2  ] n/ £ 3 _ | n / c i  _

 S2 S3 SI IS

where Is are the   reverse saturation currents.

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If the transistors are perfectly matched, and the current

gains are high enough to neglect the base currents, eqn. 2

collapses to the simple form

R, 3)

which describes the behaviour of a distortionless temperature-

independent voltage-current convertor with a transconduc-

tance uniquely set by the resistor  RE.

Note that the only hypotheses used in deriving eqn. 3

' (W)C 4

Fig.  1a  Voltage-current convertor

Fig.  \b Alternative configuration

concern the matching and current gains of the transistors;

so the result holds for any value of the input voltage  v and of

the feedback resistor  RE,  until the currents are sufficient to

keep the current gain high and validate the expression for the

base-emitter voltage drop adopted in eqn. 2. The maximum

input voltage is limited by saturation of Tr2  and Tr 4, biased

at  VCB  = 0; this limitation can be overcome by adding level-

shifting stages.

An alternative application of the proposed circuit is shown

in Fig.  \b.  This configuration has the same behaviour as the

previous one, but with a better frequency response, owing to

the common-base operation of the transistors, and without

voltage-swing limitation. The input impedance seen looking

into the emitters of Tr2  and Tr 4  is, in theory, zero, indepen-

dent of the bias current  l0.

The operation of the circuit can be also explained as a

unity-gain positive-feedback which increases to infinite

gain in the negative-feedback loop set by resistor  RE,  thus

reducing to zero any error in the voltage-current conversion.

At high frequencies, parasitic inductances can lead to a

small negative resistance between the emitters of Tr 2  and Tr 4;

so ,  to overcome stability problems,  RE  must not be too low.In the configuration of Fig.  \a,  the internal resistance of

the voltage generator can also lead to instability; a small

capacitor between the bases of Trx  and Tr 3  is sufficient to

avoid this possibility. Transistor mismatch does not alter

the performances of the circuits. In this case, eqn. 2 becomes

v + (4)

which shows that an input offset voltage is present, but the

transconductance and linearity are not affected.

Let us now consider the effect of limited current gain, with

the simplified hypothesis of current gain being equal for all

transistors and constant for any bias current.

We must consider two effects. First the variable component

of the output current is reduced with respect to the current iby a constant factor dependent on the current gain; straight-

forward analysis gives, in fact,

(5)

Secondly, the variable current / is no longer linearly depen-

dent on the input voltage. With  X = 2i/I0,  the collector

currents can be written as

(6)

+ ln = 

and eqn. 2 becomes

v-iRE+q

If the current is small, x  is small with respect to unity and we

can consider only the first two terms of the power expansion of

the logarithm; with simple mathematics, we obtain

f l + X 2a-l)

I  1-X 2a-1)

qh 3  qlo  V(8)

The overall effect is a reduction of the circuit transcon-

ductance, which becomes slightly temperature-dependent, and

the introduction of 3rd-order harmonic distortion; current-

gain mismatches will introduce additional 2nd-order dis-

tortion.

The circuit has been experimentally verified using an

integrated transistor array,* with 7?£ = 600Q and/ 0  = 500 fiA.  The measured performances are reported in

Fig.  2, which gives the peak value of the output current

Ic\—IC3,  normalised to  Io,  and the 3rd-order distortion

attenuation D3  as a function of the input peak voltage

normalised to  Vo =  RE(I0/2).  For comparison, the measured

performances of the simple degenerated differential pair made

with the same components are also shown.

80

70

60

nQ

50

40

30

—XX

 1  1

 

-io S

o

| J- 2 0

- 2 0 -1 0v /V o .  dB

148

Fig.  2  Measured output current  and  3rd-order distortionattenuation against input voltageRE  ^  600 Q ; r  =  5 fiA

•—- proposed circuitdegenerated differential pair

The measured performances show good agreement with

theory, and the improvement with respect to the simple

differential-pair stage is substantial, with a minimum number

of extra components.

RAIMONDO CAPRIO  Jst  March  1973

Laboratori Transmissione

Telettra  S.p.A.Via Trento, 30, Vimercale, Milan, Italy

Reference

1 Motorola application note AN-489,  1969

  CA3O45

ELECTRONICS LETTERS  22nd March 1973 Vol.9 No.