1220 PROCEEDINGS OF THE IEEE. JULY 1967

It should be noticed that the amplifier described so far shows a quite curious stability behavior. The pump power has to be raised until a second I region of stability is reached. Then the total value of the gain fluctuation for a given deviation of the capacitance amplitude C , is approximately the same as for the conventional reflection-type amplifier. However, the 1

I9

gain decreases with increasing pump power and vice versa. M. Pommvm

Heinrich-Hertz-Inst. f. Schwingungsforsch. b I - 1

Dt. Akad. d. Wissensch. zu Berlin Berlin-Adlershof, Germany bL2-n$-f

I REFERENCES L-g-

[I J K. K. N . Chang and S. Bloom, A parametric amplifier using lower-frequency pump

[2] K. K. N . hg, Four-termi~l parametric ampl ir , Proc. IRE (Correspondence),

[3] C. L. Hogan and R. L. Jcpsen, New type of ferromagnetic amplifier, 1. Appl. Phys.,

141 H. B. Hennine New class of Darametric a m ~ l i f i c ~ ~ enables below-siwal D U I U D ~ ~ &

ing,Proc. IRE, vol. 46, pp. 138S1386, July 1958.

vol. 47, p p . 81-82, January 1959.

vol. 29, pp. 422423, March 1958.

Fig. 2. Theoretical waveforms (not to scale). (a) Output circuit disconnected; shaded area r e p m u stored charge. (b) Output circuit connected.

i , = VAt - tl)/L1 + i , ( t l ) . . - . . - (51 M. Pommreit, Einige allgermhe Eigmschaften der quasientartetcn parametrischen

IEEE Inrerna~l Conv. Rec., pt. j, pp. 90-97, 1563.

VersWer b%crer Ordnunrr Wiss. Z. Elekrrorech., vol. 7, no. 2, PD. 65-79, 1966. id = I , cos ot - i,,

[6] -, Em neuarliger tiefnfroquent gequmpter parametrissher V&tiirker, Whs. Z. Elekrrorech., vol. 7, no. 4, pp. 193-208,1966. and the diode accumulates a charge q(t) :

[7] -, Der ELiniluss der zweiten und dritten Kapadtatshannonischen auf die Eigen- schaften des quasientarteta parametrischem Vierfrequenzenverst&kers, Wiss. 2.

[8] -, Dk Dcutung pp Elektrorech., vol. 8, DO. 2, pp. 65430, 1 9 6 6 .

&I R ~ e ~ e ~ ~ I & k r s t i i r l t e r als H~hfreq~CnZ- bandliltcr. Hochfiequenzrech. und Elekrrwkusr., vol. 71, pp. 19&205, June 1%2.

191 -. Parametrische Netnuerke m i t n Hilfsfreouenzen. Wiss. 2. Elekrrorech.. vol.

q(t) = f id dt. . ,

[IO] -, Halbleiterdiodemvetiirker, in Elektronisches Rouschen, pt. 2, H. Heifer, 7, no; 3, pp. 3 ~ 9 , 1 9 6 6 . At time t , given by q(t,) = 0, the total charge becomes zero ; the diode Ed. Leinzix: B. G. Teubner Verlamm.. in DI~SS. becomes an open circuit and a current pulse is produced in R, as in Fig.

Frequency Mpltiplier Using a ChargeStorage Diodemanhht iveCirca i t

A b S t T U C i - - A n a d j % k i s a r r i e d o P t f ~ U 8 f r e e P e n e y ~ ~ 8 cbfgegtorrrgediodeianidoctivecircPitExpwdom.rederivedfor ~ u d p o w e r ~ f o r t h e a s e n h e r e t b e d i o d e ~ i p ~ T l e r e s J t s 8 r e v e s i E e d e x p m ~ j .

The circuit to be considered is shown in Fig. 1. It consists of a charge- storage (step recovery) diode biased in the reverse direction by a battery V, with an inductance L, and a resistance R, in parallel. This network is fed from a current source ip at an input angular frequency a, and the output at ng is determined by the series circuit L,, C, where R2 is the load resis- tance. Unlike previous work on this type of circuit [l 1, [2], we assume the diode depletion-layer capacitance to be neghgibly small. This could occur, for example, in low-frequency multipliers, as is borne out by the experi- mental results.

Fig. I . Basic circuit

Let us assume, to start with, that the output circuit L,CR, is removed. The diode starts to conduct at a time t , given by :

While the diode is conducting, the currents in L , and in the diode are, respectively,

formed part of a contract with the D.G.R.S.T., Paris. Manuscript received February 15,1967 ;.revised March 3 and April 3,1%7. The project

Initial Transient The current i, ( a s s u m e d constant during the transient at a value I,,)

divides itself between L , and L,. By classical methods we fiad the voltage across L1 :

uL1 = - (Igl + ZLl)Rle-R1(1+u)riL2 (5 )

where a=L,/L, and I , , is the current in L1 at the start of the transient. This negative pulse is shown in Fig. 2(b) for R,noL, >> 1. For this condi- tion, the pulse is completed before C has time to charge appreciably. At the end of this initial transient, the current I,, in L, is given by :

Second Phase

The second part of the transient consists of an oscillation of the cur- rent iL2 ia the circuit L, , L,, R , where

i,, = I,, cos wbt, (7)

ob being the angular frequency deterained by L,, L,, C in series. The voltage on L , is thus

where Y,=o&5,1L,. After a time approximately equal to x/ob, for high harmonics [Fig. 2(b)], the voltage on L, becomes positive; the diode starts conducting and oscillations occur in L,C due to the energy stored in L,. The analysis is completed by writing the recurrence relations, incorporat- ing the initial current in L,C. For the particular case of Q t n , where Q is the loaded Q factor of the output circuit, we obtain:

q = (2 + a)- (9) w = qa(1 + a)/(4nn20L2) (10)

VJV, = nJ(1 + a/2). (11)

PROCEEDINGS LETTERS 1221

"Ll

'LI

Fig. 3. Measured waveforms; input: 5 MHz; output: 25 MHz. r,=6 ns, r , = 3 0 0 ns, C,=5pFat - 6 V . L , = 2 . 4 p H , L 2 = 1 . 2 p H , R , = 6 0 0 Q R , = 1 6 R . H o r i z o n t a l s c a l e : 40 nsjsquare: vertical scale: VLL: IO V.square, i , , =60 mhsquare; i,,:30 mA,'square.

The measured waveforms of Fig. 3 show the two transient phases, although as expected the initial transient is prolonged due to the non- negligible recovery time and capacitance of the diode. The following are typical of the results obtained :

~~

Theoretical Experimental

W (mw) VJ v, 13 11.5

1.7 rl 0.3 1

4.5 0.2

The complete analysis suggests that this type of circuit would be par- ticularly suited to high-order, moderate-power multiplication, whereas the noninductive type of circuit [3] gives excellent results for low-order, high-power operation.

ACKNOWLEDGMENT Thanks are due to J. Rouh of C.S.F. for carrying out the experimental

D. J. ROULSTON' Depart of Elec. Engrg. University of Waterloo

Waterloo, Ont., Canada

work.

RJFERENCEs

[l ] R. Hall, S. Hamilton, and S. Krakauer, "Impulse shunt-mode harmonic generauon," Digest of Technical Papers, 1966 Intefnat'l Solid-state Circuits Conf. .. pp. 6 6 1 .

121 R. Thompson, "Steprecovery diode frequency multiplier," Necrronics Letters, vol. 2, pp. 117-1 18, March 1 9 6 6 .

[ 3 ] D. J . Roulston, "Frequency multiphcation using the charge storage effect: an analysls for high efficiency, high power operation," Inrernat'lJ. Hecrronics. vol. 18, pp. 73-86, January l%5.

' On leave from C.S.F., Puteaux 92, France.

Capacitive Feed Tluongh Calculatiom m MOSFET IC's Abstract-Compbg between lnigbvoltage dock bes a d high-hpd-

ancedifiPsedregiom.hMOSFETICsaobesi@kmt.Aaetbodis described for CPlceLting the voltage fed onto a modhear pn jmction capac- i t a n c e f r w r a m e t a l ~ l e d . ~ i s b a s e d a p w a l o a d l i n e dram 08 the Q-Y-. . .

There exists, in integrated circuits (IC's), the possibility of sigmficant coupling between a metal interconnect lead on an oxide surface and a diffusion underneath. The situation is especially critical in MOSFET IC's because of high impedance levels, thin oxides, and the high-level signals normally encountered. This letter describes a method for calculating the signal fed onto a voltagedependent p n junction capacitance from a metal lead.

Figure 1 shows the equivalent circuit used for the feed through analysis. C , , a fixed MOS capacitor, has a typical value of 0.2 pF/mi12 for loo0 A of thermal silicon-oxide. C, is a voltagedependent p n junction capacitance.

Vin - '1 T MOS CAPACITOR,LINEAR ov

OUTPUT

P-N JUNCTION CAPACITANCE

FUNCTION OF VOLTAGE ACROSS THE CAPACITOR

Fig. I . Equivalent circuit for feed through analysis.

Since any input step produces equal charge on both capacitors a simple load line approach on a Q-V plot will yield the solution for the output voltage as illustrated on the graph of Fig. 1. Equal charge, occurring at the intersection of the two lines, may be read from the ordinate while the voltage distribution between the capacitors (required to produce the equal charge) is read from the abscissa. The load line equation may be obtained by summing voltages around the equivalent circuit.

Via = Qtic, + V'ut. (1) To use the graphical approach described here it is necessary to know the Q-V relationship for a pn junction. An expression for charge added to a capacitor (over and above the charge due to diffusion potential) is

AQ = 1 "A+:tmld(4 + V') (2) where V, =applied voltage, 4 =diffusion potential, CIMd = total capac- itance per unit area, AQ = charge per unit area.

Equation (2) says that the added charge, AQ is the area under the C-V curve between the voltage limits of 4 and V, + 4. The problem now reduces to finding a relation for Cl4 that can be integrated. There are two possible approaches. First, C versus Vcan be measured plotted, and mechanically integrated. Second (the approach used in this letter), an approximate ex- pression can be derived for cad as a function of (4 + V,) and substituted into (2).

0

Assume

Qta.1 = K ( 4 + %'A)''" where

Qmld = total charge/unit area, K = constant.

Since

then

c,,,,, = - (4 + V,)'l'"'- K n

By knowing the doping levels involved, a curve of Ct,,,=f(4+ VA) can be obtained (see Lawrence and Warner'). Plotting on log-log paper and reading the intercept and slope yields K / n and (l /n)- 1, respectively. Placing (3) into (2) and integrating results in

AQ = K ( 4 + V,)"" - K(4)"". (4)

Manuscript reoeived April IO, 1%7 Bell Sys. Tech. J. , vol. 39, pp. 389403 , March 1960. H. Lawrence and R. M. Warner, Jr., "DifT'used junction depletion layer calculations,"