RD-R73 714 THE DEVELOPMENT OF A HIGH SPEED EXPONENTIAL FUNCTION L'1GENERATOR FOR LINERR.. (U) DEFENCE RESEARCHESTRBLISHENT OTTAWA (ONTRRIO) J F MICKERL ET RL.
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Defence nationate
THE DEVELOPMENT OF A HIGH SPEED EXPONENTAL
FUNCTION GENERATOR FOR LINEARIZATION OF .%MICROWAVE VOLTAGE CONTROLLED OSCILLATORS (U
by
J.F. Mickeal, J.J. Renaud and M.R. McMillan ""-,Radar ESM Section
Electronic Warfare Division DTIC 'E L ECT E
,, NOV 4 1986
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DL"M~nONSTATEMENT A
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DEFENCE RESEARCH ESTABLISHMENT OTTAWATECHNICAL NOTE 88-3
PCN October 198531B10 Ottawa
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ABSTRACT
Voltage Controlled Oscillators used in radar signal simulators
usually employ piecewise approximation linearizers to compensate for non-linear frequency versus voltage tuning characteristics. A linearizer was ~developed which closely approximates an exponential (frequency/voltage)
(voltage/current) characteristic of a p-n junction to provide exponentiallinearization in a simple, thermally-stable, wide band circuit.
RESME
Les oscillateurs A tension variable couramment employ~s pour lasimulation de signaux de radars utilisent habituellement un circuit delin~arisation par point pour compenser leur r~ponse non lintaire tension f
versus fr~quence. On d~veloppa donc un circuit de lin~arisation qui serapproche tr~s pras de la courbe exponentielle (fr6quence/tension) que V'on 1
retrouve chez plusieurs oscillateurs. Ce circuit, d'une grande largeur debande, utilise la caractfiristique (tension/courant) du biais avant d'unejonction P-N pour g~n~rer la r~ponse exponentielle requise pour lalinearisation.
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TABLE OF CONTENTS
Page
ABSTRACT/RESUME ........................................................... iii V.- -,
TABLE OF CONTENTS ......................................................... iv
LIST OF FIGURES ........................................................... v
1.0 INTRODUCTION ......................................................... I
2.0 VCO CHARACTERISTICS................................................... .
2.1 Linearization Methods ........................................... . .32.2 Exponential Linearizer Circuit Realization ...................... 62.3 Temperature Dependence .......................................... 6
3.0 EXPERIMENTAL RESULTS ................................................. 10
3.1 System Function Measurement ..................................... .103.2 Long Term Frequency Stability ................................... 103.3 Linearizer Step Response ..................................... 10'
4.0 CONCLUSIONS ......................................................... 19 ' -
5.0 REFERENCES........................................................... . 19
APPENDIX A VCO FUNCTION MEASUREMENT METHOD ............................... 21APPENDIX B EXPONENTIAL LINEARIZER THEORETICAL DERIVATION ................. 25 ' .,..
APPENDIX C EXPONENTIAL FUNCTION GENERATOR HARDWARE REALIZATION ........... 29
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LIST OF FIGURES
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FIGURE 1 - Non-linearized VCO Transfer Function .......................... 2
FIGURE 2 - Required Linearizer Transfer Function ......................... 4
FIGURE 3 - Theoretical Fit............................................... 5
FIGURE 4 - System Exponential Fit ........................................ 7 .-
FIGURE 5 - System Error .................................................. -
FIGURE 6 - Conceptual Exponential Function Generator ..................... 9
FIGURE 7 - Actual Linearized VCO ......................................... 11 .,/.
FIGURE 8 - Actual Linearized VCO - Error ................................. 12
FIGURE 9 - Linearized VCO Long Term Frequency Stability (8 GHz) .......... 13 .
FIGURE 10 - Linearized VCO Long Term Frequency Stability (9 GHz) .......... 14 .-.
FIGURE 11 - Linearized VCO Long Term Frequency Stability (10 GHz) ......... 15
FIGURE 12 - Linearized VCO Long Term Frequency Stability (11 GHz) ......... 16"
FIGURE 13 - Linearized BCO Long Term Frequency Stability (12 GHz) ......... 17
FIGURE 14 - Response of Linear Approximator and ExponentialFunction Linearizers .......................................... 18
S. FIGURE Al - Experimental Measurement Set-up ............................... 23
FIGURE Cl - Exponential Function Generator - Circuit Diagram ............... 33
FIGURE C2 - VCO Driver Amplifier.......................................... 35 II'
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1.0 INTRODUCTION
Voltage Controlled Oscillators (VCO) are used in low power radar signal % %simulators to produce programmable signal scenarios. Providing coincidentpulses are not required, one VCO can generate a large number of classes ofradar signals using microprocessor and discrete hardware to obtain fastexecution. For each emitter pulse, the oscillator is quickly tuned to therequired frequency and the signal is switched to the output for the durationof the pulse. Simulation of pulse compression emitters can be effected byapplying a linear analog ramp to the tuning input of the VCO. During thepulse duration the ramp continuously changes the VCO frequency, thereby
causing a "chirp" signal.
A VCO should provide a frequency set-on accuracy of about 0.05% ofcarrier frequency and respond to the tuning voltage demand in a fewmicroseconds. .
Commercial VCO's usually consist of a varactor-tuned, microwave,frequency source and a non-linear voltage amplifier called a linearizer. The
linearizer compensates for the non-linear voltage versus frequency function of %
the oscillator to achieve an approximate linear relationship. The linearizeris based on a straight line approximation technique and is often found to ring
in response to a tuning voltage step thereby causing long settling times.
Measurements on the oscillator alone indicated that in many cases the
required input versus output voltage function of the linearizer is exponentialin nature, therefore an exponential function could be employed as a linearizer.Also the exponential function is continuous compared to that of the straightline approximator. Therefore, for chirp signals, a more gradual frequency %.%
slope could be obtained which eliminates spurious responses at the breakpoints of a linear approximator. _4r-
This report deals with the development of the exponential functiongenerator and concludes with measurements on accuracy and temperaturestability. 0. %
2.0 VCO CHARACTERISTICS
Before consideration is given to various techniques to linearize a VC(,
it is necessary to determine the VCO tuning voltage versus frequency functlon.
As outlined in Appendix A, a microcomputer was used to step the tuning volt .w,through all possible values, and for each value, the resultant frequency ofthe VCO was measured using a frequency counter. Such a measurement is shownin Figure 1 for an X band VCO. The desired response, of course, is the .- jIndicated straight line.
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Since a linoarizer module would be inserted between the tuning voltagesource and the tuning input to the VCO, the combined function of the '% N
linearizer and VCO can be written as:
F = G [h(v)] (1)
where: h(v) is the gain characteristic of the linearizer and G is the VCOfunction, for example, that presented in Figure 1. ' -V p
From equation 1, it is clear that the inverse of G, will yield h(v), therequired linearizer function. The required linearizer function shown inFigure 2 was derived from the data plotted in Figure 1 by using an Inversionalgorithm. Note the frequency range 8-12 GHz is replaced by 4096 count, (C),values, as described in Appendix A.
2.1 Linearization Methods
Typically, the curve of Figure 2 is approximated by several linearsegments using analog circuitry. However, in order to achieve areasonable accuracy, a considerable number of segments are required.
It is also apparent that for a large number of segments (10 ormore), complex circuitry will result. In radar EW simulators, it Is alsorequired that the tuning speed be high (less than 5 microseconds), andhence the complex circuit must also have fast rise and settling times.
From measurements taken on a commercial linearizer delivered with aVCO module, the bandwidth was measured to be 100 KHz and the settling '.
time was observed to be of the order of 100 microseconds due to a ringingeffect.
Stimulated by the above mentioned problems, it appeard that thecurve of Figure 2 could possibly be approximated by an exponentialfunction of the form:
Vo = a (exp(b Vi)-I) (2)
where: Vi is the input voltage to the linearizer
a and b are constantsand Vo is the output voltage of the linearizer. ..
As outlined in Appendix B, the constants can be found numericallyand the resultant exponential linearizer function is plotted over therequired function as shown in Figure 3. It is evident that a good fitwas obtained because it is almost impossible to delineate between theexperimental and theoretical curves.
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The final step, however, is to consider the response of thelinearizer and VCO modules together as a system. Substituting equationinto equation 1, and using the measured data set for the VCO function %
(G in equation 1), the desired linearized VCO function can be obtained
and is shown plotted over the ideal straight line function in Figure /, -
Figure 5 details the error versus frequency one might hope to achievewhere the maximum deviation is about 30 MHz.
2.2 Exponential Linearizer Circuit Realization
The exponential function is based on the non-linear property of -I
semiconductor diode where the current/voltage relationship is given by:
i = io (exp(v/(n Vt))- 1) (3)
where: io is the reverse leakage current of the diode
v is the voltage applied across the junction
n is 2 for silicon
and Vt - T/11,600
where: Vt is the "volt equivalent of temperature"
T is the temperature in degrees Kelvin.
In the conceptual circuit of Figure 6, Q1 is the non-linear elemenL
given by equation 3 where the base-emitter current i is multiplied by t,,-o
current gain of the transistor. The other components in Figure 6 perforinversions and current to voltage transformations to achieve the function
given in equation 2. Appendix C provides details on the derivation ofthe circuit form, and given a set of equations for the circuit values, an
exact circuit is realized.
2.3 Temperature Dependence
As noted from equation 3, the linearizer will be temperature ..
dependent. In the actual realization, the transistor pair, Ql and Q2were selected to be on a single substrate. The substrate was pre-heated
to a regulated temperature using other spare transistors on the array.
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3.0 EXPERIMENTAL RESULTS
The performance of the exponential linearizer can be evaluated on thebasis of an analysis of the system function (frequency versus input voltage)data, long term frequency stability data and the response of the linearizer toa voltage step input. The following sections deal with these measurements.
3.1 System Function Measurement
The system function (linearizer and VCO combined) was determined byacquiring a group of 4096 voltage-frequency data values as shown inFigure 7 together with the linear function. Figure 8 shows thedifference or error between the experimental results and an ideal linear '--
function indicating a +/- 100 MHz deviation, or about 1% error.
3.2 Long Term Frequency Stability
Long term Frequency stability was measured using 5 selected tuning. voltage values which were recorded in a burst with 50 msec between each
successive value. The burst recording was made every 15 minutes forapproximately 75 hours. The graphs shown in Figures 9 to 13 indicate thefrequency drift for each of the selected tuning voltages. The maximumfrequency drift is approximately 4 MHz over 75 hours evaluation period.
3.3 Linearizer Step Response
Measurements were made on the response of a 100 KHz bandwidthcommercial linear approximator and the exponential function linearizer.Figure 14a shows the response of the linear approximator to a step demandfor the VCO to shift from 8 to 10 GHz frequency. This linearizer has atransient response lasting for a period of about 60 microseconds. Themagnitude of the initial oscillations produced a peak-to-peak frequency .-.modulation of approximately 60 MHz on the 10 GHz carrier.
Figure 14b shows the response of the exponential function to thesame step signal and the linearizer output has reached a fixed voltage inabout 3 microseconds. No significant frequency modulation was observedon the carrier signal 3 microseconds after the step was applied. "
These results demonstrate that using the wide-band exponentialfunction generator, not only is intra-pulse FM reduced but also many "q
• radar signals at different frequencies can be generated per unit time* because of its fast settling time.
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4.ui CONCLIUSIONS
'Ihe expnetal linarize r perm its the VCO t o respond~ LO he 3er'ild I
Piven frequency in a few microseconds. This is an importanr fac ter sinct, onc,
VCO can then Ihe used to generate a large number of radar sigitals )n differe~vfrequencies per unit time. J
Tn addition, the exponential linearizer provides a methodl( t- -irlHev -r % ~ first-order linear approximation to the frequency versuis volhage
ch~iracteristic of many types, ot VCO's. The discont inui r ie -.- n- ite 1ipifecowise linearizer are avoided which otherwise can he of drhcoiwern when generating linear frequency modulated or chirp) r.0,ir II
The accuracy achileved wi th the exponent ial I Ineari zer 1 comnctit rv ,piecewi se Ilineari zers and I t Is relatively simple to desigi' and iol jusi , roptimum performance.
~eponenttal linearizers, the final frequency correction uses ligital
selected and run.
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VCO FUNCTION . .r
?4EASUREMENT KETHIOD
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* Measurement MethoO
*VCO d ata is obt ai ned undor tIe cont roI o!- jesrrr1i u r I tas shown in Figure A-1. Commanded froquence e are coiiverted .-1 ala Ivo itages, using a 12 hit D/A converter where a~ f/A coinot of +01r p resent s an output vol tage range of 0 t o 10 vo 1t s. .,he D/A ntTconnected to the input of either the linearizer tinder test or d i r .:t-1v nr
* p.%
VCO Lo obtain the non-linearized VCO function shown in Figure 1 nf thereport. A frequency counter is employed to measure the freqiuency of t I tCesignal from the VCO. The counter performs a measurement in apprO~imve,1v 5(msec with a frequency resolution of 0.25 MHz.
* Measurement Process
The measurement_ process i s accurate ly I ime(' such itr(r!measurements can he oltral ned. Initially, tle D/A is -o t ;Iintof zero aind for each measuirement event, I ho foillowinp .' *rt (-Y a 0co:
1. The a/A is tuned to some requested frequency.
2. The frequency coarnter is directed to make a .s.c
3. After the measurement delay of 50 msec, the DA. is -,in,_d b,
the vase frequency (a D/A count of 0).
4. An intra-pulse delay time is initiated p rogit:!-a b I .ro.
250 riser).
5. cpon the I ntn a-p t1se time-out, the pro-css d -c_ o: -.t ,
other test frequeno,,.
VO o ntr-plse dlav tileme VC s used t o s inFigre ., ,he V(Y) among- several emitters. During times whoert n. o- i ic i
i q pre n yt , th VCO Is norm I Iv tuned to thoue bte f r, .
VCO Freqienc data Ls collect ed in mrenpt, whin : ap o i 1 i.i* :sin i ncreasi ng sequence ot prograimmel frquonci, I 'I~uri
se nth J fer. Each frequoncy n the s02 quenf- i[ esIuren .' F frequency itreme(t II-ti I t he iu fma"ured. A specefable group delay time i s the n ii t i id
m-ott, be next group of measurements is taken. DA i t i t i ,-I to 65,nn0 seconds ar e possible.
AcquireO data is tranfrred to hos computer it r jweit
-,torage and detailed analys is.
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VCO Fnction
In order to determine the gain characteri.;tic of a lin,,iriztr using, -
technique outlined in Appendix A, It is necessary to measure the e-act %response of the VCO to all possible input voltage values. Since a 12 bit )/A % , %
converter is employed, there are 4096 possible set-on frequencies.Experimental data was collected using a AF value of 1.
Inverse VCO Function
The input voltage (v) to the linearizer is derived from a D/Aconverter.
Let the galn characteristic of the linearizer be tv), H erefork.,one may express the VCO output frequency as:
F = G [h(v)] (ih.
where: C, relates the VCO frequency to the initial voltage, V,
and includes the effect of the linearizer gain and VCOcharacteristic.
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In all further discussion, the voltages applied t o the lirneari7er,-and the VCO are considered in D/A count units, where v is aiT. integervalue which ranges from 0 to 4095.
It is required that some h(v) be found such that:
F = a. + alv (2,W-
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ai ere: a o and al are some set of constants that connect, the end -. ,points of the curve, as shown in Figure 1 of the report. .' .
Given the measured VCO function data set, for some v (taken aq a ,-of 4096 D/A values), equation 2b is evaluated aid the data .;et issearched for the corresponding frequency element. The associated i ut %
T/A value is therefore tho required h(v).
Exponential Curve Fit
Given the data set (ref. ligure 1), whore the i ' h .;impl, i. -f iil'. i.: ,.(i,Ci), assume a best fit can he obtained by: . ."
Ci = a (exp(hi)-l), 9-.
where: C1 is the i'th fitted valuea and h are constants "'I Is the i'th input integer value .
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then the i'th squared error is:
s2 = (C I - a (exp(bi)-l)) (4b)
Given that the end points C(4095) and C(O) are made equal t(, the dati ,,.
values C(4095) and C(0), a least squares fit can be performed on h as frllr.:%
2 4095 2- (C - a (exp(bi)-l)) (a T Pxp(h 1 )) = 0 (5h) . ':
ab i=0
where for some b, the constant, a, is defined as: %
a = 4095/(exp(4095b)-l) (6,b) . ..
Defining the upper end point as C(4095), then the lower end point
automatically connected for I = 0.
Solving equations 5b and 6b numerically:
a = 0.0 788 39x4095
h = 2.616229/4095
where a and b are shown normalized to the full scale value of -
The actual and fitted curves are shown in Figure 3 of the report. ic.error curve shown in Figure 5 indicates that a relatively good fit can b-.-obtained with a maximum deviation of about 30 MHz or 0.3% at mid-bandfrequency.
System Error
The curve fit problem outlined above was performed on the requiredlinearIzer gain characteristic. Although the resultant least squareserror has been minimized on that curve, the "system" error should beconsidered where the system is composed of the combination of the -linearizer and VCO.
Recall that equation (lb) describes the system frequency versus;input voltage function and now that h(v) is known, values of frequency .*.can be plotted against v. The error curve, Figure 5 in report, shows .I 11Zalmost equal error variation about the zero error axis, indicating thatthe original fit on the required gain characteristic was reasonable.
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Exponential Function Generator
Conceptually, the exponential function generator is based on the* current/voltage relationship of a diode. In the circuit diagram shown in J
Figure 6, the exponential function generator Is composed of a matched . 4
differential transistor pair (QI and Q2). The collector Current of Ql is madeconstant by U2. Tr'e input is v2 and the output is 12. U3 converts i2 to Voutand Ul performs an inversion and offset of the Input signal Vin.
The current/voltage relationship of a diode Is given by:
I =to (exp(v/(n Vt)) - 1) (c
where: io Is the reverse leakage current of the diodev is the voltage applied across the junctionn is 2 for silicon
and Vt = T/11,600 (20)
- where: Vt is the "volt equivalent of temperature"T is the temperature In degrees Kelvin.
Assuming that exp(v/(n Vt)) 1 for a forward biased diode, replacing1/(n Vt) by a constant k and assuming some constant ambient temperature:
i i o exp(k v) (30)
.5- Assuming that the current gains and reverse leakage curronts, life anid in,respectively, In the differential pair in Figure 6 are matchod, the currentsi1 and 12 are defined as:
11 = f to exp(k (v2 - v3)) ('40
12 = ito exp( k (-v3)) Sce
- ~ From equations 4c and 5c, (hfe to) can be extracted such that:S*
li fe to =11 exp (-k(v2 - v3)) 1 2 exp (-k(-v3)) (6c)
Solving equation 6c for 12 yields:
12 - 11 exp (-k v2) (7c~)
where: il is a constant due to U2.
Inversion and offset of VInr is performed hy III and as.,o,-iat ed 'is .s* Referring to Fig. 6, VI is attenuated by the R5 and R6 network-.;. Assm ii in* Input voltage range of 10 volts, V2 in terms of Vin (,.10 he writ tci als:
v2 = k2 (10- Vin)( T c * *
where: k2 R6/(R5 +R16)
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i2 = il exp (-k (k2 (10 - Vin)))o r
i2 = 1 exp (-10 k k2) exp (k k2 Vin) (c
The output amplifier, U33, sums an offset current (los) with C) ind
converts, the result to Voult by:
Vout = R8 WI - ins) ((~
;in~d when combined with equation ()c yields: 4
Vout =R8 i1 exp (-10 1 k2) exp (k k2 Vi n) RS ios
whir' can be written in the form:
'lout = a (exp (h Vin)- Z) (11r)
14hevre: . = R8 Pxp (-10b)= k k?'
k =1/(n Vt)*k= R6/(R5 + R6)
nd = R8 los/a
To olhtain the correct form of the exponential function we set
RS ios -
a
!1l~ on I c is of the desi red form as used in b e previoiis :;tct i I-,
ismi ng the matched conditions an; noted and a constant ambient tempera! tr.
'I rctit Realization
The resi st or values i n t he c Ircui t of Fi gure 6 ;1re- dote rm i nod 1> Ion reference voltages of +/- 12.0 volts for +Vref and -Vrprespt-ct ivelv. Referring to equation 8 c, UIl will providle thc require'function (lO-Vin) if we set: >..
RI = R3 = 10 K
2= 12' K.%
Tn I he f ollowing derivat ion, theit equat ions of I ntc Ie.;t I ro:
\T0 a (cxp(b Vin) -1) (i 2 c)
whorea RR il ex)p(-10 h) (13)
% % %.. . .. . .*.
% **-**%*
-32-
and R8= k k2 (1 4 ) :R8Ios/a = 1I1~) -.
where:k = l/(n Vt)n = 2 for silicon
Vt = T/11,600
to 10 vls
a = 0.78839 ~* ~b =0.261623I ~and selecting R4 to be 3.3 K, d.
ii 3.634 ma., a constant, due to U2.
From equation 13c, i .
RB8 2.9687 K.
Assuming a fixed ambient temperature of 70 degrees Kelvin, equation
14c yields:
k2 = 0.015471
and for R6 =100 ohms, R5 =6.363706 K.
From equation 15c, R9 45.3352 K, to obtain the required valtie of offset 0
current ios. ~
Fxponentlal Function Generator - Detailed Circuit
Intedetailed circuit diagram of Figure C-1, 01 performss the inpiltIneso and offset, U2 maIntains a constant collector current through
Qi, QladQ2 form the differential pair and U4 provides thecurrent-to-output voltage conversion.
In order to maintain the substrate of Qi and 02 at ipproximately 71)
degrees Celslits, Q3 Is used as a temperature sensor. Xs notoul for the
RCA CA 3046, Vbe varies as -1.9 my per degree C, therefore the circitl o'
B U5 and Q6 drives Q4* and Q5 to heat the substrate such that Vhe through
6 tho divider R10, R11, results in a null input to U5.
Cl and r2 provide additional frequency compensation to P'? and !'4L
re-spectively such that a 0.5 microsecond rise time can he achievedwithout ringing. C3 prevents temperature "hunting".
Metal film resistors are used as noted to minimize temperature drift.
NO%
%
-33 -
4.
*+Vref +Vref
3.3kpR 4 *68k R13
I C68p.
VinReIT 82- Vu
2 4
10k e hL82-- 02
U44
R15.
%: +107L15+r
04 re CA3046 04 15 R162
-155 791 RVr768a
~e . 2 ~1 . + (-2V -RB15072-I~.'
R1 4 ~13 Gain Adj. A28 %mf
3- 1
hL
-34-
Output Driver Amplifier.
To achieve the fulI tuning range, t he VCO requi res ;ai i npu rav -,,approximately 6 to 45 volts. The circait of Figure C- 2 transforms th(lInearizer output range of 0 to 10 volts to the required %'CO drive. n,,.to the limited unity gain bandwidth of 01, the circuit of I'] provl.e'; ifixed gain with Cl used for additional frequency compensation.
The gain of the driver amplifier is given by:
G = 1 + (R6/(R3 + (R4 R5)/R4 + R5)) (1-.
and is set to approximately 4.5. The overall gain is accur.itelv set h%-
R]4 in Figure C-i. The overall offset is controlled hv P , shown ,. -
Figure C-2. %,.
Calibration
Before using the calibration procedure outlined below, thelinearizer should be powered up and allowed to stabilize forapproximately one hour. Using a temperature probe and thermallv
conductive paste, measure the case temperature of U3 In Figlire C-1. Avalue of approximately 65 degrees C or higher should be found and it no',
adjust RI1 to obtain the correct temperature. The differential pairsubstrate must operate higher than the highest expected ambienttemperature.
Three adjustments are required to calibrate the linearizer - VCrsystem. The procedure is interactive and assumes that suffici, tt warmu'.time has expired. Three accurately known input voltages ire reqiitr,, I .
tone the VCO to the lowest, mid and highest frequencies. These. art "respectively 0, 5.0 and 10.0 volts. Initially, trim-pots ca;, he! ,,i in-
place of R6 and R14 in Figure C-1 and R5 in Figure C-2 with initialsettings as indicated.
Assuming an X band VCO, the corresponding three freqtioncv v.-lii,,'should be 8.0 Glz, 10.25 GHz and 12.0 Cllz. Using the gain and offset %adjustments, perform the following steps: .,\,
1. Set the input to 0 volts and adjust the gain pot for 8.0 G4p7.
2. Set the input to 10.0 volts and adjust the of Ese. pot ft I .(1 I- -" %
3. Repeat steps I and 2 tintil the correct frequonclo,; at,' t md. . .
With the end-points correctly set, input 5.(I vl t t .11A Ii :t ' K.
rurve adjustment pot for 10.25 Gliz. Then Input 0 vnlt- in aInd l n t I 1. -
gain pot for 8 Gliz. Alternate these two adjustments nt il he ,',:r. .
frequencies are obtained.
% ,% %.
. P - - n . 1
,l , " * 2". ¢,tr;, "_ " ;. .... ..._ .
+-65V
F422
aw. Vout
Vin > -V%-
Re*.
12.1 kR3' 2.7
RIO-
I * I56
RS''.
4 1 4-.- k*. r R-
-Vref___ ~*
%
-36b-
ajuqtment I frorW.Repeat steps 1, 2 and 3 and then perform the curve iad )~'rt
required. A few of the above iterations will be required i re oV e
achieve an accurate result.
The resistor values obtained after calibration can then be fixedwith metal film networks to minimize thermal drift. Those indicated inFigures C-i and C-2 were obtained from the above procedure.
It is assumed that end-point adjustments in trim-pot form areavailable within the D/A module and would be subsequently set to providea slightly greater frequency range than the 8 to 12.0 CHz obtained fromthe above calibration procedure. Any further end-point corrections andof course the final error correction can then be removed digitally.
'6 %
%A
-37-
['NCI.ASl1 1) ~j
DOCUMENT CONTROL DATA H & D
)'E4ENCE RESE'ARCH ESTABLISHMENT OTTAWA, UENCLASSIH LDDepartment of National Defence,Ottawa, Ontario KIA 0Z4 Canada- 4
THE DEVELOP'MENT OF A HIGH SPEED EXPONENTIAL -t'NCT I]) (d HGIN kATR F"ORL.INEARIZATION OF MICROWAVE VOLTAGE CONTROLLED OSCILLATORS (U)
TECHNICAL NOTE-
MICKEAL. JIames F., RENAUD, lean-,Jacques, MCMILLAN, '1y R.
A OCTOBER 1985 W\* 40
Un- 1 S
trqec u svla e nin hararsiis A~~ I 5 ,r%, .;d(:
whc e po peeis approximatio n exinenari l to comenvvat :,. :rnon-itnari
totind in many VCO's. This linearizer uses the forward biased (voltage/currcint)characteristic of a p-n junction to provide exponential linearization i!n a
imlthermally-stable, wide band circuit.
* 7I,-
V'--
VOLTAE CONROLLE OSCILATOREXOETA
- 38 - IZER
ANALOG CqRCUIT
RADARSIGNA SIMUATOR
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