Measurement Techniques,Vol.42, No. 9, 1999

A M A C R O M O D E L O F AN O P E R A T I O N A L A M P L I F I E R FOR MODELLING MEASUREMENT CIRCUITS WITH PULSED S I G N A L S

A. N. Andreev, V. A. Kazakov,

UDC 621.396.6:681.3

a n d A . V. S v e t l o v

A modified macromodel of an operational amplifier for the PSpice program and a method of calculating its parameters are considered. The macromodel enables one to reproduce authentically specified values of the asymmetrical ma.rimum rate of growth of the output voltage of an operational amplifier.

The metrological characteristics of measuring circuits with pulsed signals are largely determined by the dynamic properties of the integrated operational amplifiers, which form part of these circuits. One can investigate the properties, optimize the parameters and synthesize circuits containing operational amplifiers at the level of mathematical models of the circuits which use modem methods of circuit modelling. The most widely used of such methods is the PSpice software package produced by the MicroSim Corporation [I, 2] and the Design Center and Design-Lab programs based on it for designing analog, digital and analog-digital devices [3]. To operate in the PSpice environment, leading design companies who design and produce analog integrated microcircuits (Texas Instruments Inc., Linear Technology Corporation, Analog Devices Inc., etc.) have prepared a library of macromodels of the operational amplifiers they manufacture. The macromodels of Russian operational amplifiers can be set up using the Parts program [2], which forms part of the PSpice software package. From the values of the manufacturer's parameters of the operational amplifier introduced by the user, this program enables one calculate the parameters of its macromodel in the framework of the standard topology of Boyle's model [4, 5]. The reliability of the results of modelling circuits containing operational amplifiers is largely determined by how much of the initial data entered by the Parts program user corresponds to the actual parameters of the real operational amplifier. Investigations have shown that to ensure good agreement between the modelling results and the experimental data one must specify the frequency and time parameters of the operational amplifiers, given in the manufacturer's literature, used to set up the macromodel. In particular, the actual values of the maximum rate of growth of the operational amplifier output voltage are usually different for voltages with positive and negative slope and are considerably higher than the minimum permissible value of its parameter given in the manufacturer's literature. The unit amplification frequency of an operational amplifier must be indicated for the specific value of the correction circuit capacitance, whereas in the manufacturer's literature the unit amplification frequency of an uncorrected amplifier is usually given. The parameters of an operational amplifier can be determined comparatively simply experimentally - for a specific sample of an operational amplifier or the average one of the batch of microcircuits employed. In particular, when setting up a macromodel of the K544UD2A integrated operational amplifier, as a result of experimental investigations of a selection of 20 microcircuits, we chose a sample, the values of whose dynamic parameters were close to the mean values for the sample examined: for a unit amplification frequency fl = 8 MHz, with the internal correction frequency included, the maximum rate of growth of the output voltage with a positive slope + SR = 32 V/psec, and for a voltage with a negative slope - SR = 45 V/psec. Using the Parts program and the standard topology of the PSpice software package, we set up a macromodel M 1 of this operational amplifier. In addition to the experimental data indicated, we used the following manufacturer's data: - power supply voltage +15 V; - power consumed under static conditions 0.21 W; Translated from Izmeritel'naya Tekhnika, No. 9, pp. 26-29, September, 1999. 858

0543-1972/99/4209-0858522.00 9 1999 Kluwer Academic/Plenum Publishers

UoutV,//~

10 50-

-10 0

/ I

I

I

1.2

1.6

2.0

I

2.4 t, psee

Fig. 1. Time diagrams of the voltage at the output of a K544UD2A operational amplifier operating as an inverting amplifier:. 1) experimental data, 2) the M1 model (+SR = 32 V/psec and -SR = 45 V/psec).

input bias current 100 pA; - constant voltage gain 20,000; - in-phase signal suppression coefficient 30,000: - low-frequency output resistance 120 f2: high-frequency output resistance 60 f~: maximum short-circuit current 120 mA: internal frequency correction capacitance 15 pF; phase delay at unit amplification frequency 60 ~ An estimate of the reliability of the representation of the properties of an actual operational amplifier by its macromodel can be obtained by comparing the results of modelling and of an experimental investigation of the process by which the output voltage of an inverting amplifier is established. In Fig. I we show time diagrams of the voltage at the output of an inverting amplifier with a gain K = 1, obtained using the K544UD2A operational amplifier with internal frequency correction, when a bipolar rectangular pulse with an amplitude of +9 V and a leading edge duration of 0.04 psec is applied to its input. As can be seen from Fig. 1, the M1 macromodel, generated by the Parts program, in accordance with the standard topology of the PSpice software package, does not enable one to reproduce the specified results, which differ in the value of the rate of growth +SR and --SR of the operational amplifier output voltage. At the same time, if these values are the same, the required value of the rate of growth is reproduced fairly accurately. The unauthentic representation of the asymmetry of the rate of growth of the output voltage does not enable the standard macromodel of an operational amplifier in the PSpice software package to be used to model measuring converters of the parameters of electric circuits with pulsed signals. Hence, it is an urgent problem to design a modified macromodel of an operational amplifier, which enables arbitrarily specified values of the rate of growth +SR and -SR of the output voltage of an operational amplifier to be represented reliably. It is desirable to construct a modified macromodel of an operational amplifier based on a standard macromodel, in order to be able to calculate its parameters using the Parts program of the PSpice software package. The maximum growth rate of the output voltage SR in the standard macromodel of an operational amplifier is determined by the source current ISS and the capacitance of the frequency correction capacitor C2: SR = ISS/C2. If different values of the maximum growth rate of the output voltage with a positive slope (+SR) and a negative slope (-SR) are specified as the initial parameters of the operational amplifier, a capacitor CSS, which models the output capacitance of the current source ISS, is introduced by the Parts program into the operational amplifier macromodel. This gives a more exact representation of the growth rate only tbr the in-phase signal, and hence the specified ratio of the rates +SR and -SR is not reproduced. To eliminate this drawback a diode [6] can be connected in series with the capacitor CSS and then, for the same polarity of the output voltage of the operational amplifier, the total capacitance C2 and CSS will be charged by the source current ISS, while for the other polarity only C2 is charged. As a result, one obtains different growth rates. This solution can only be used to model the edges of similar pulses, since the diode is unable to discharge the capacitance CSS. -

-

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062 VEX

" 21 1 $12 31

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Fig. 2. Modified macromodel of the operational amplifier.

In the macromodel of the operational amplifier, developed by specialists at the Linear Technology Corporation [7], the values of the maximum growth rate +SR and -SR are specified by the change in the dynamic mode of operation of the charging current of the correction capacitor. For this purpose, the current of an additional current source, controlled by the voltage from the differential output of the input stage, is added to or subtracted from the source current ISS. For all macromodels of this type in the operational amplifier macromodel library of this company, a characteristic feature is the fixed value of the ratio of the growth rates: +SR/-SR = 0.5. To eliminate this constraint and to ensure the possibility of specifying arbitrary values of +SR and -SR, one can use the following method of modifying the operational amplifier macromodel and the method of calculating those of its parameters to be changed. In the modified operational amplifier macromodel (Fig. 2), the following are additionally introduced: a voltage-controlled current source (VCCS) GSS, a voltage-controlled switch $1, and a resistor RS1. A differential voltage [U(12) - U(I 1)], taken from junctions 12 and 11, is used as the controlling voltage for GSS and $1. The method of calculating the parameters of the modified macromodel involves the following stages. 1. Using the Parts program, the parameters of the operational amplifier macromodel are calculated with the same values of the rates (+SR) 1 and (-SR) I, equal to the required value +SR of the maximum growth rate of the output voltage of the modified macromodel. The values of the current (ISS) 1 and the resistance (RSS) 1 are fixed. By modelling the voltage repeater with this operational amplifier, to the input of which a voltage jump +U is applied (the amplitude of the jump should ensure that the output stage of the operational amplifier is saturated), the voltage difference [U(12) - U(I 1)] 1 is determined at the instant of time corresponding to the maximum growth rate +SR. 2. The parameters of the operational amplifier macromodel with the same values of the rates (+SR) 2 and (--SR)2, equal to the required value -SR of the maximum growth rate of the voltage of the modified macromodel, are calculated. The values of (ISS) 2 and (RSS) 2 and also the voltage difference [U(12) - U(11)] 2 at the instant of time corresponding to the maximum growth rate --SR when the voltage jump - U acts are determined. 3. The following system of equations is set up:

ISS + KGss[U(12)- U(I I)] l = (ISS) 1, 1

f

(1)

ISS + KGSS [U(I 2 ) - U(I 1)]2 = (ISS)2 ,J as a result of solving which one determines the value o f l S S - the source current ISS of the modified macromodel, and also the value of KGSS - the transfer constant of the voltage-controlled current source GSS. 860

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Fig. 3. Determination of the differential voltage [U(12) - U( 11)] 1.

4. The resistance of resistor R S S is assumed to be equal to (RSS) 1, while the resistance of resistor RS1 is calculated from the tbrmula RSI = ( R S S ) L( R S S ) 2 / [ ( R S S ) L - ( R S S ) 2 ].

(2)

5. The parameters of the voltage-controlled switch S I are chosen: V O N - the on-voltage of the switch, V O F F - the off-voltage of the switch, R O N - the resistance of the on-switch, and R O F F - the resistance of the off-switch. 6. Using any text editor, the description of the operational amplifier macromodel obtained in Section 1 by this method is edited. The value of the current (ISS)I is changed to the new value ISS: the lbllowing descriptions of the new components of the operational-amplifier macromodei are introduced: GSS RS1

10 4 12 I i KGs S 31 99 RS1

I0 31 12 11 SX model SX VSWITCH ( V O N = V O F F = + R O N -- R O F F = ).

S1

We will use this method to design a modified macromodel of the K544UD2A integrated operational amplifier with internal frequency correction and the following parameters: +SR = 32 V/psec and - S R = 45 V/psec. 1. Using the Parts program, we set up a macromodel (M2) of an operational amplifier with (+SR)I = (--SR)I = 32 V/psec. We fix the values (ISS) l = 480 pA and (RSS) 1 = 416.7 k~. As a result of modelling a voltage follower, at the input of which a voltage jump +U = 9 V is applied, we find [U(12) - U(I 1)]! =-0.663 V (Fig. 3). 2. Using the Parts program, we set up a macromodel (M3) of an operational amplifier with (+SR) 2 = (-SR) 2 = 45 V/psec. We fixed the values (ISS)2 = 675 pA and (RSS) 2 = 296.3 k.Q. As a result of modelling a voltage follower, at the input of which a voltage jump - U = - 9 V is applied, we found [U(12) -U(11)]2 = 0.92 V. 3. By solving the system of equations, we determine the values of the parameters of the modified macromodel: ISS = 561.674 l.tA and KGS S = 123.18 pA/V.

-

4. We take R S S = 416.7 k.Q and RS1 = 1025.5 kX'2. 5. We choose the parameters of the switch SI: V O N = 2 mV, V O F F = 1 mV, R O N = 1 m~z and R O F F = 1 m f L

6. The description of the modified macromodel (M4) of the K544UD2A operational amplifier with a connected internal frequency correction has the following form: * M4 operational amplifier "macromodel" subcircuit * connections: non-inverting input, inverting input, positive power supply, * negative power supply, output .subcktM4 1 2 3 4 5 cl 11 12 4.330E-12 c2 6 7 15.00E-12 dc

5

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vlp 91 0 dc 20 vln 0 92 dc 20 .model dx D (Is = 800.0E-18) .model jx NJF (Is = 50.00E-12 Beta = 1.184E-3 Vto= ~ I ) .model sx VSWITCH (VON = 2E-3 VOFF = IE-3 RON = IE-3 ROFF = 1El2) .ends The method was also used to set up macromodels of the K544UD2A integrated operational amplifier with external frequency correction. When introducing the initial parameters of the amplifier into the Parts program, the value of the correction capacitance (C2 in Fig. 3) was found as a result of the series connection of the capacitance C c of the external frequency-correction capacitor and the capacitance of the internal frequency correction (15 pF). The values of the unit-gain frequencYfl and the maximum growth rate of the output voltage +SR and -SR, which are used as the initial parameters, were found experimentally. We show in Table 1, as an example, the parameters of the modified macromodels of the K544UD2A operational amplifier for two values of the external frequency correction capacitance. In Fig. 4 we show the results of modelling of an inverting amplifier with a gain K = 1, based on the K544UD2A operational amplifier, predetermined by the modified macromodels: M4 - for internal frequency correction, M5 - with C c = 68 pF, and M6 - with Cr = 22 pF. A bipolar rectangular pulse with an amplitude of + 9 V was applied to the amplifier input. The values of the output voltage growth rate of the amplifier obtained by modelling correspond to those values of +SR and -SR which were specified when setting up the operational amplifier macromodels. The modified macromodels of domestic operational amplifiers, designed taking the experimentally measured parameters into account, give good agreement with the results of modelling with experimental data. This enables these models to be used to simulate measurement circuits with pulsed signals.

862

TABLE 1.

Parameters of the Modified Macromodels of the

Operational Amplifier Parameter

Model M5

Model M6

68

22

12.3

8.9

10

13.2

39.5

50.5

58

75

578.86

537.97

141.92

139.43

Capacitance of the external frequency correction Cc, pF Resultant correction capacitance C2. pF Unit gain frequencyf1, MHz Maximum growth rate of the output voltage with positive slope + SR, V/psec Maximum growth rate of the output voltage with negative slope - SR, V/psec Source current ISS of the modified macromodel ISS, pA Transfer constant of the VCCS GSS KGSS, ~A/V Resistance RSS, kO Resistance RSI, kf2

411.6

445.0

878.69

916.93

10 5-

O- 21~ -10

1

I

I

I

1.0

1.5

2.0

t, psec 2.5

Fig. 4. Results of modelling of K544UD2A operational amplifier: 1) model M4, 2) model M5, 3) model M6.

REFERENCES 1.

2.

PSpice User's Guide. MicroSim Corporation, La Cadena Drive, Laguna Hills (1989). V. D. Razevig, The Use of the P-CAD and PSpice Programs for Circuit Modelling on a Personal Computer [in Russian], Radio i Svyaz', Moscow (1992).

5.

V. D. Razevig, The Design Center (PSpice) System for the Circuit Modelling and Design of Printed Circuits [in Russian], SK Press, Moscow (1996). G. Boyle et al., IEEE J. of Solid-State Circuits, SC-9, No. 6, 353 (1974). A. G. Aleksenko and B. I. Zuev, Zarubezh. Radioelektron., No. 8, 22 (1977).

6.

A G. Aleksenko et al., Macromodelling of Analog Integrated Microcircuits [in Russian], Radio i Svyaz', Moscow

7.

(1963). W. Jung, Electronic Design, No. 20, 71 (1990).

3. 4.

863