FUNCTIONAL AND DETERMINISTIC TUNING OF HYBRID

Electrocomponent Science and Technology1978, Vol. 5, pp. 79-89

(C) Gordon and Breach Science Publishers Ltd., 1978Printed in Great Britain

FUNCTIONAL AND DETERMINISTIC TUNING OF HYBRIDINTEGRATED ACTIVE FILTERS

G. S. MOSCHYTZ

Swiss Federal Institute of Technology, Zurich, Switzerland

(Received June 15, 1977)

The two main methods of tuning hybrid integrated active filters, namely functional and deterministic tuning aredescribed. Functional tuning implies the fine adjustment of an active network that is assembled and in operationso that its transmission characteristics (e.g. gain or phase response) can be monitored during the tuning process.One or several resistors are selected as tuning elements and these are adjusted (e.g. by laser, anodization, sand-blasting, "postbox" selection of discrete resistors) until the desired response is obtained. Deterministic tuninginvolves the fine adjustment of individual resistors to values which are analytically predicted. The prediction isbased on network equations which include parasitic effects and in which those component values that are not to beadjusted are obtained by measurements on the (non-operational) manufactured circuit. Manufacturing tolerancesand parasitic effects are included in the comprehensive set of equations whose solutions provide the final adjustmentvalues of a few ’tuning resistors’. Accuracy bounds and limitations of the two tuning methods are given and the prosand cons of the two methods are discussed. Finally it is suggested that a well balanced combination of the twomethods may well provide the most efficient and least complicated solution to the tuning problem in hybridintegrated networks.

1. INTRODUCTION

As active hybrid-integrated filters are increasinglybeing developed for modern communicationsystems, 1-7 so the question of how to tune them tospecifications most efficiently, and at minimum cost,is becoming ever more important. In practice twobasically different tuning methods can be distin-guished, namely functional and deterministic tuning.8

Functional tuning implies tuning the criticalparameters of a network while it is functional, i.e. inoperation. Because the network is assembled as foroperation in the final system, any parasitics builtinto the network are automatically taken intoaccount and "tuned out" during the tuning process.Functional tuning is generally iterative, particularlyif the tuning steps are interactive (Figure 1). Thenumber of iterations will increase with the degree oftuning accuracy required. The larger the number ofiterative tuning steps, the more time consuming, andtherefore the more costly, the tuning process will be.Functional tuning will generally be preferable forlaboratory purposes and when production quantitiesare moderate or low.

Deterministic tuning implies tuning, or trimmingto value, individual components of a network aspredicted by a combination of comprehensive net-work equations (in which parasitic effects are taken

79

into account) and by component measurements(Figure 2). The solutions of equations (generallyobtained by an on-line computation facility) providethe values of the components to be tuned. Tuningis carded out "to value", hence it makes nodifference whether the network is operational or not.Since the components to be tuned are invariablyresistors, this method consists of "resistor trimming",in contrast to the tuning of network characteristics(e.g. amplitude, phase, frequency) that occurs infunctional tuning. The method is simple ("to-value"trimming of resistors is essential in any hybridintegrated circuit manufacturing plant) and rapid inexecution (generally very few, if any, iterations arerequired). However, powerful computer programswill be required to solve the nonlinear networkequations which must take first, and often secondorder parasitic effects into account. Deterministictuning is the more efficient of the two methods, butthe necessary expenditure of an on-line computationfacility, and the initial computational effort required,can generally be justified only by very high pro-duction volumes.

In practice it will very often be found useful tocombine functional with deterministic tuning. Theinitial adjustments will be carried out bydeterministic tuning, where the values are obtainedfrom either the idealized network equations or from

80 G.S. MOSCHYTZ

Runtuned RtunedTuning Resistor R

ing Tolerance

FIGURE Functionally tuning to a parameter value No with the tuning resistor R.

N

N (R)///

/AR

Runtuned

// tuning tolerance

Rtuned

FIGURE 2

Tuning Resistor R

Deterministically tuning to a parameter valueN with the tuning resistor R.

F (ala2 an

INPUTSIGNAL

R

O-i CHARACTERISTIC TUNING PARAMETERS; Rc. TRIM COMPONENTS

FIGURE 3 Functionally tuning the characteristic tuning parameters a with the corresponng resistors Rai toobtain the specified function F(ai).

TUNING OF HYBRID ACTIVE FILTERS 81

those containing at most first-order parasitic effects.To overcome more subtle second-order parasitics, afine-tuning step is then undertaken in which thecircuit is operational (i.e. assembled and powered)and a functional adjustment of one or more of thecritical parameters is carried out. In this way thecomputational complexity inherent in deterministic-only tuning can be considerably reduced.

2. FUNCTIONAL TUNING

Functional tuning is based on a set of networkequations in which the changes of the specified net-work characteristics Fj,j-- 1,2 m are related toincremental changes in the components xi, 1,2,..., n, by the sensitivity matrix, hence:

| x;m Iwhere the sensitivities are defined by

dx .Hence, if a (i 1,... n) are the characteristic tuningparameters of a network function F(ai) and Rai arethe corresponding tuning resistors (Figure 3), thentuning the parameters from a +i to a will adjustthe network function from its initial formF(ai + i) to the desired form F(ai). tting

dai/aiS’a dRaj/Rajwe then obtain the sensitivity relations:

(3)

dai/a

cla./a.

"Ra:z "i" ’Ran

Si Si i

_Ra, ’Ra=’’’’Ran LdRalRan](4a)

or

---] (4b)

where [S] is the sensitivity matrix.In order to allow for a noninteractive, and hence

noniterative, tuning procedure the sensitivity matrixmust be a diagonal matrix, meaning that all off-diagonal matrix elements must be zero (Figure 4a).In practice this will rarely be the case. However, itmay be possible to arrange the sensitivity matrix suchthat it is triangular with the upper triangular elementsbeing zero (Figure 4b). For each network character-istic ak there is then a tuning element Rak thatleaves all previously tuned parameters aj Q" < k)unaffected. The tuning sequence is critical; itresults directly from the sensitivity matrix after thelatter has been arranged in triangular form. Theobtained sequence provides a single-pass (or one-shot),noninteractive tuning procedure requiring no itera-tions. If a triangular matrix in the form of Figure 4bcannot be obtained accurately, it must beapproximated by arranging the matrix elements suchthat they decrease in value to the right of thediagonal (Figure 4c). In this way, the number oftuning iterations can be minimized.

Consider, for example, a second-order networkpossessing two conjugate complex poles p x, :-o +j. The corresponding transfer function willhave the form"

N(s)T(s) (5)

(s + p )(s + p: )

Assuming that the two poles p and p: are specifiedand must be tuned for, we now derive the matrixequation corresponding to (4) with respect to the nresistors in the network. (Capacitors cannot beadjusted in hybrid-integrated circuits and aretherefore not considered as tuning components.)We obtain:

"dPlPl

dp:

P:

II +jOll

21 +jr21

S,

Ul 2 +iV12 Uln

U2 2 + iV2 2 U2n

(6a)

82 G.S. MOSCHYTZ

D AGONAL MATR X(a)

ARB TRARY NONITERA,T

TUNING SEQUENCE

Is]=

al \,x Rai \

Ra 2 \

ai \RaJ \ ’S an \

x’Ran

TRIANGULAR MATRIX(b)

PRESCRIBED NONITERATIVE

TUNING SEQUENCE’

FIGURE 4

\ 0alSRal a2 " S\ Rai]\ SRa \\ 2 \

\

l,.ai \ "..b Raj

I. Ran

PRESCRIBED [TERAT VE

TUNING SEQUENCE

Ro .--, Roz...R, Rn

Roi > R

Functional tuning strategies a) non-interactive b) interactive, one-pass c) general interactive.

R2=2R_=I ._3

RI=2 C2 c,

Via mV%/V

i ’"/- Vout

CI=I R3=II":

FIGURE 5 Second-order bandpass network.


or, in matrix form"

d__p_p [u + ]v] -- (6b)P

It can be shown9 that"

j (7)p cop qp

where cop X/a2 + 2 and qp cop/2a. Thus itfollows that in (6):

ui SRP (8a)and

vi -(4q 1)-1/z. R (8b)In terms of the pole frequency cov and the pole Q,qp, we therefore obtain from Eq. (6a)"

ldcoP!ull ul2 ...Un R

dwp dRnu2 u22...u2.p Rn

and

Lqp

(9a)

-W/4q’-

dR ]

(9b)Since Pl and pz are complex conjugate, the variationsof copl, cop and qp,, qp will not be independent ofone another and we need consider only the variationdcop/cop and dqp/qv.for a second order network.

Let us now consider the second-order active band-pass network shown in Figure 5. The voltage transferfunction is

s sT(s) K K

(s + p l)(s + P: ) +qp

(10)In practice, cop and qp rather than the pole pair Pland p will be specified, since the former areaccurately measurable quantities. In addition, theconstant K will be specified, although in general witha much wider tolerance than cop and qp. Deriving thesensitivity matrix with respect to the five resistors of

the network, we obtain"

dK/Kdcop/copdqp/qp

-1 0 0 -1

-0.25 -0.25 -0.5 0 0

0.25 -1.75 1.5 1.5 -1.5

-dR /R -dRz /RdR3/R 3

dR4/R4

dRs /R

(11)We must now rearrange the sensitivity matrix inEq. (11) so as to provide a tuning sequence com-prising three resistors and requiring a minimumnumber of iterations. (Clearly neither a purelydiagonal nor a triangular matrix can be obtained.)The best we can do is with the resistors R1, Ra andR4, namely:

dcop/cop -0.25 -0.5 0 dRcop/Rcopdqp/qp 0.25 1.5 1.5 dRqp/Rqv

(12)where RK =RI ,Rwp Ra andRqp =R4. Theoptimum tuning sequence is then R (K) R a (cop) -R4 (qp!kwhereby a slight error will be accrued in Ksince SRqp :fi: O.

3. ACCURACY CONSIDERATIONS FORFUNCTIONAL TUNING

When tuning for the frequency response of a network,we have the choice (inthe case of minimum-phasenetworks) of tuning to a specified amplitude or to aspecified phase. The question is which of these twophysical quantities provide more convenient indicatorsfor the tuning process. If we tune for an amplituderesponse as indicated in Figure 6a we are concernedwith the variation of the amplitude a (e.g. in dB) at aparticular frequency coi with respect to the variationof a corresponding tuning resistor Rai, thus:

[da(coi) t,eirca(’’i)] [ dRai (12a)

84 G.S. MOSCHYTZ

a)

INITIAL TOLERANCEBEFORE TUNING

FIGURE 6

DEGREES]

Functional tuning indicators a) amplitude b) phase.

where:dot

dR/R(12b)

Similarly, tuning for a phase response (Figure 6b), thecorresponding relationship between the phase (i)and the tuning resistor Ri will be"

[dq()l [/R(i)l [1Vi Ri j (13a)

where

S- dOdn/R

(13b)

At first sight it would seem that the sensititiesEq. (12b) and Eq. (13b) will determine whether the

amplitude a or the phase is a preferable tuningindicator for a given minimum-phase network. How-ever, it can be showna that no matter what the net-work, the phase is always a more accurate indicatorwith which to tune the response of a network. Infact the tuning accuracy of the amplitude responseof a second-order all-pole network is within+2A% or _+0.2ACdB, when trimmed by means of aphase meter with an accuracy of -+A. This is

independent of the pole Q. Thus, with the attainablephase accuracy given by A degrees, the resultingamplitude accuracy in dB will be:

A < 2A% 0.2A [dB] (14)It follows that a phase error corresponds to a

0.2 dB error in amplitude. Phase meters with up to


0.1 phase accuracy are available at prices considerablylower than voltage meters with comparable accuracy(i.e. 0.02 dB). It follows that wherever possible,functional tuning by phase is to be preferred overtuning by amplitude. The pole frequency errorresulting from a phase error A is then:

fP [%1-Tr 100/Xq (15)

fp 360qp qpwhere A is measured in degrees and qp is the pole Q.Note that the higher qp the smaller the frequencyerror resulting from a given phase error. Thus, with0.1 phase error, the frequency error will be -0.1% ifqp and -0.01% if qp 10.

The accuracy of qp associated with a phase errorof A degrees can be shown to be independent of qp.It is approximately given by:

Aqp[%] --3.5A (16)

qpprovided that the phase is measured at the pole-frequency phase, pluslorlminus 45 degrees.

Consider, for example, the lowpass amplitude andphase characteristic shown in Figure 7. From thecorresponding transfer function

2

T(s) K Cl:’

sqp

(17)

we obtain the amplitude response

a(Co) In T(/’co) (18a)

-45

-90

-135

-180

FIGURE 7 Amplitude and phase characteristic of a second-order lowpass network.

and the phase response:

(co) arg T(d’Co) (18b)To tune for the specified cop and qp values, we tunefor -90 at the frequency cop/2r using an appropriateresistor Rto and for -45 (or -135) at the

Pfrequency co4 s/2r (or co, a s/270 using an appropriateresistor Rqp. With a phase meter accurate to withinA degrees, the errors in amplitude, frequency and qpwill be as given by Eq. (14), (15) and (16) respectively.K can also be tuned for. Remember that an error inK implies an error in the dc gain of the network.

4. DETERMINISTIC TUNING

For a given network, the deterministic tuningprocedure follows the flow-chart presented in Figure8. Thus for the second-order lowpass network shownin Figure 9, whose transfer function was given byEq. (17), we proceed as follows8

1) Derive the three characteristic networkparameters K, cop and qp as a function of the circuitcomponents, i.e.

K= fr(fl, R,,R2, Ca, C4)

Cop fwp(R,R2,R4, Ca, C4)qp fqp(fJ, R,R2,R4, Ca, C4)

2) Measure the capacitors Ca, C4 and the closed-loop amplifier gain/3

3) Compute the following resistor values as afunction of quantities that are either specified ormeasured, i.e.

R fR, (K, cop, qp, Ca, C4, [3)R2 fR (K, cop, qp, C3, C4, fl)

R4 fR, (K, COp, qp, Ca, C4, t3)4) Trim resistors R t, R2 and R to the values

computed under 3).

At this point some comments seem in order.The equations derived in step 1) and 3) are tuning

equations and not design equations. The derivationof the design equations precedes the tuning processand determines the nominal value of each componentincluding the gain . Since there are more componentsthan there are design equations, various optimizationcriteria can be taken into account in the design, suchas minimum sensitivity, minimum gain-sensitivityproduct, ease of tuning, minimum component spread,upper and lower bounds on resistors and/or capacitors

86 G.S. MOSCHYTZ

MEASURECAPACITORS(INCL, LOSSES)

COMPUTE RESISTORVALUES FROM

NETWORK EQUATIONS

TRIM RESISTORSTO VALUE

MEASURE RESPONSEAND COMPARE WITH

NOMINAL

RECALCULATERESISTORS BASEDON MEASUREMENTS

FIGURE 8

TRIM RESISTORSTO NEW VALUES

Deterministic tuning sequence.

etc. In any event, the design, or nominal values of eachcomponent are known before the tuning process isbegun. Thus, in the example of Figure 9, although thenominal value of is known, the actual value ofobtained in. manufacture is measured in step 2) bymeasuring resistors R6 and R7 (Note that at thispoint the amplifier is assumed to be ideal.)

For the Sallen-Key type circuits shown in Figures5 and 9,/3 is not made equal to unity, but is larger(e.g. between one and two) if tight tolerances arespecified for qp. If necessary a final functionalcorrection of qt can thereby be carried out withoutaffecting the pole frequency p. Although this entailsthe inclusion of an additional resistor, namely R7(R6 is required to balance DC offset), this is a smallprice to pay compared with the increase in yieldafforded by the possibility of a final touch-up tuningstep. The deterioration of gain stability incurred bythis slight increase in gain is negligible o in hybrid-integrated filters, due to the very close resistortracking obtainable with either thick or thin filmresistors. The combination of deterministic andfunctional tuning implied here will be furtherdiscussed under section 6.

The measurement of the capacitors (i.e. C3 andC4 in step 2) above) should preferably be carried outafter the (chip) capacitors have been assembled on thesubstrate. (In the case of thin film capacitors there is,of course, no other choice). This permits parasiticcapacitance and assembly drift to be taken intoaccount during the measurement. Although methodsexist for the accurate measurement of individualcapacitors when they are connected to additionalcircuitry8, the preferred way of overcoming thisproblem is to provide provisional capacitor contactsto the substrate edge. These permit the measurement

R7=R R6= (8-i) R

C R4

FIGURE 9 Second-order lowpass network.


FIGURE 10 Frequency-dependent gain of an operationalamplifier.

FIGURE 11itor.

logC

Frequency dependence of a thin-film eapac-

of either single capacitors, or combinations of parallelor series pairs, as required for the subsequentcomputations.

To attain a one-pass tuning procedure, parasiticeffects due to nonideal circuit components mustgenerally be taken into account in the networkequations derived under step 3 above. This complicatesthe required computations considerably. The mainparasitic effects that must be contended with are:

i) Non-ideal characteristics of the active devices(e.g. frequency dependent gain of the operationalamplifiers). Referring to Figure 10, this means thatinstead of using the constant gain/30 in our equations,we must use/(s), thus:

o (s) - (19)s +OOa

ii) Losses and frequency dependence of capacitors.Thin-film capacitors, for example, are both lossy dfrequency dependent. If the loss of a capacitor Ci istan i, then, instead of Ci, we must approximate Cias follows:

CiCi Ci Ci(1 _/6i )+ j tan 6 + j6

(20)Instead of frequency-independent capacitors, thin-film capacitors will be frequency-dependent accordingto the relationship:

C C(w) Ce-wrc (21)whereby the time constt rc characterizes thetecology used. Assuming that the value of C(w) ismeasured at two frequencies (see Figure 11), the valueof C(p) can be obtained by extrapolation as follows:

log C(wp) log C(,) + rc(p ) (22)where

log C(=)/C(w )r (23)

2 1

iii) Parasitic capacitances on the circuit substrateand resistive losses along conductance paths.

These parasitics must be taken into account, tothe extent that the response of the final assembledcircuit is to be as accurate as if it had been tunedfunctionally. In doing so, the computations requiredunder 3) above become rapidly more complex, theequations highly non-linear and of third, or evenhigher order. With increasing complexity, onlynumerical solutions by computer can be expected,whereas with ideal components, analytical solutionsmay be obtained. A more detailed discussion of thetuning of hybrid-integrated circuits with nonidealcomponents is given elsewhere. 8

5. ACCURACY CONSIDERATIONS FORDETERMINISTIC TUNING

Using the deterministic tuning procedure, the accuracyattained depends on the accuracy with whichcapacitors can be measured, and resistors can bemeasured and trimmed. Assuming a worst-casemeasuring error of AC/C for all capacitors and anequal worst-case trimming error of zLR/R for allresistors, we obtain a frequency error given by

< + -- (24)O9 max max max

With a 0.1% accurate capacitance bridge and acapability of trimming and measuring resistors towithin 0.05%, the worst-case frequency error will be0.15%.

The accuracy with which the capacitor losses aremeasured will also effect the frequency accuracy,adding a term to the two in Eq. (24). Assuming a loss-measurement error of Ai, we obtain the additionalterm:

AW ( )1+--- A8 (25)w 2qp 4qp

88 G.S. MOSCHYTZ

This error is significantly smaller than the onerepresented by Eq. (24). Measuring the capacitorlosses to within 10% accuracy (i.e. A6 0.1) andassuming a pole Q of only 2 (i.e. qp 2), thefrequency error given by Eq. (25) is 0.02%.

In general, any function F that is tuned to valueusing a resistor RF will be accurate to withinF(1 +- AF/F), where

ARF (26)

and F/RF is the trimming and measuring accuracyof the resistor RF. Consider, for example, the case inwch qp is to be tuned deterministically by adjustingthe closed-loop gain . This, in turn, is determined bya resistor ratio say Ro/R, whereR is the trimmingresistor (e.g. R6 or R v in Figure 9). The qp accuracyfollows as

(27)

For the network of Figure 9 Eq. (27) becomes:

qp q RwhereR R6. If Rv were used forR the expressionon the right-hand side of Eq. (28) would be negative,a

With a capability for measuring and trimmingR tothin 0.05% accuracy, and th the typical values offl 2, q 0.4 and qp 20, We obtain qp accurately towithin 1%. Note that with currently availablemeasuring equipment deterministic tuning can readilycompete with functional tuning in terms of accuracy,profided that a sufficiently thorough computationaleffort and adequate computer facilities are invested inthe process.

6. COMBINING DETERMINISTIC WITHFUNCTIONAL TUNING

Because deterministic tuning entails only componentmeasurement, computation, and resistor trimming, itis the preferred tuning method, provided theproduction quantities are large enough to justify theinitial computational effort (deriving the networkequations including parasitic effects) and the cost ofon-line computation facilities. Very often, the initialcomputational effort can be significantly reduced byderiving the equations of the idealized network and,after initial deterministic tuning, correcting theresulting error by a small number of functional tuning

SELECT n OF TOTAL N RESISTORS,

R[,i =1,2 n FOR FUNCTIONAL

TUNING (TYPICALLY 1 OR 2)

MEASURE CAPACITORS (ONLY i ACCU-RACY REQUIRED, LOSSES NOT NECESSARY)

COMPUTE RES STOR VALUES

FROM SIMPLE (IDEALIZED) NETWORKEQUATIONS

TRIM RESISTORS R TO VALUESRE(1-E),TRIH REMAINING RESISTORS

TO FINAL VALUE

MEASURE RESPONSE,F NE-TUNE FUN,,CT ONALLY US NGRESISTORS R

FIGURE 12 Combining deterministic with functional tuning.

steps. This procedure, outlined in Figure 12, eliminatesthe numerous and time-consuming iterative tuningsteps generally required by the purely functionaltuning procedure. It accomplishes this by reserving asmall number (typically one or two) appropriateresistors for a final touch-up, or vernier functionaladjustment after the circuit has previously been"coarse adjusted" deterministically using simple, i.e.idealized, network equations.

7. SUMMARY

The two main tuning procedures used for hybrid-integrated active networks have been described. Theirmain characteristics are summarized in Table I.

Functional tuning is conceptually simple and veryeffective in that all stray and parasitic effects of apractical circuit can be tuned out "in situ" with thecircuit in operation. The main disadvantages of the


TABLEThe main characteristics of functional and deterministic tuning

Functional Deterministic

Network in operation Network not in operation

Conceptually simple, directly Computationally complex,applicable requires considerable pre-

liminary analysis

Trim resistors to specified Measure components andfunction values (e.g. compute resistor values, trimamplitude, phase, frequency) resistors to computed values

Requires accurate phase and Requires accurate resistor andfrequency measurements capacitor measurements

Tuning steps generally Resistor trimming non-interactive interactive

Parasitic effects tuned out

Iterative (time consuming)

Parasitics included in networkequations

One-to-two trimming steps

Tuning sequence derivablefrom sensitivity matrix

Requires on-line computationfacilities and nonlinearequation solving routines

Suitable for lab-purposes and Suitable for high productionlow production quantities quantities

method are the required time consuming iterationsand the high-accuracy measurements of suchparameters as phase, amplitude and frequency. Suchmeasurements are often alien to the typical hybrid-circuit manufacturing facility which is equipped forhigh-accuracy resistance and capacitance measure-ments only. Functional tuning thus becomesparticularly useful for prototype and lab purposesand for low-quantity production. Deterministictuning is based on the more sophisticated concept ofpredicting all relevant parasitic effects analyticallyand, by a combination of component measurementsand computations of resistor values, trimmingresistors to value such that the required networkresponse is obtained. It is thereby a "one-shot"

process in that, ideally, each resistor need be trimmedonly once. The disadvantages of the method are thecomplexity of initial computation and the luxury ofon-line computing facilities. Given sufficiently highproduction quantities, however, such initial outlaysin brain and computer power may readily be justifiedand subsequently amortized. Finally, for the mostcommon "intermediate" situation where productionquantities are neither so high nor so low as to obviatethe question of the most suitable tuning method, acombination of functional and deterministic tuningseems to offer the best results.

REFERENCES

1. G. S. Moschytz, "FEN Filter Design Using Tantalum andSilicon Integrated Circuits",Proc. IEEE, 58, Apr. 1970,pp. 550-566.

2. J. Gensel, R. Meissner, V. Seidel, "An Active RC Filterfor PCM Systems", Circuit Theory and Applications, 1,1973.

3. W. B. Mikhael, L. K. Keys, "Standardizable Low-PassVoice Band Hybrid Circuit Filters for PCM Communica-tion Systems," IEEE Journ. Solid State Circuits, SC-10,4, Aug. 1975, pp. 229-236.

4. W. Kraushar, U. Rickli, M. Schulthess, L. Sltry, "MFCFilter",Hasler Mitteilungen, 3, Sept. 1975.

5. "Aktive Filter fllr PCM-Systeme in Dickschichttechnik",NTZ Kurier, NTZ 28 (1975), H.11.

6. R. Jeffers, D. G. Haigh, "Active RC Lowpass Filters forf.d.m, and p.c.m. Systems",Proc. lEE, t20, 9, Sept.1973, pp. 945-953.

7. R. A. Friedenson, R. W. Daniels, R. J. Dow, P. H.McDonald, "RC Active Filters for the D3 Channel Bank",BSTJ, 54, 3, March 1975, pp. 507-529.

8. G. S. Moschytz, Linear Integrated Networks: Design,Van Nostrand Reinhold Co., New York, 1975, pp.376-425; pp. 499-538.

9. G. S. Moschytz, Linear Integrated Networks: Funda-mentals, Van Nostrand Reinhold Co., New York,1974, p. 238.

10. G. S. Moschytz, "The Operational Amplifier in LinearActive Networks", IEEE Spectrum, 7, July 1970, pp.42-50.

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FUNCTIONAL AND DETERMINISTIC TUNING OF HYBRID

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