- Email: [email protected]
Desensitisation of the oscillation frequency of RC sub-audio sinewave generators with single resistor control
0026-269218411503-0018 $6.00/0
Desensitisation of the oscillation frequency of RC sub-audio sinewave generators with single resistor control by A. R. Saha*, S. Nandi**, and R. Nandi* *Jadavpur University, India **Women's Polytechnic, Calcutta, India
This communication aims at treating the problem of desensitising the oscillation frequency (too) of a class of resistor-controlled sub-audio generator (SAG) on the basis of the examination of the t o o - s e n s ~ e s of such oscillators that are implemented through two main synthesis techniques. The study includes a new canonic SAG configuration realised with these techniques along with a comparison of their to0-sensitivities which finally derives the insensitive design.
1. Introduction Stable and insensitive realisation of low-frequency sinusoids at sub-audio bands finds applications in the measurement and test instrumentation of circuits and systems possessing relatively large time constants. In particular, sinewave generators covering 0.1 to 10 Hz are of interest for applications in geophysical, physiological and bioelectronic systems. 1 The synthesis of RC sub-audio generators (SAG) with single resistor control is receiving attention at present. 2s The general basis in all such synthesis techniques is to introduce some time constant enhancement factor by appropriate feedback in the network. Wilson 6,9 has shown that the use of low-pass positive feedback for a SAG realisation increases to0-sensitivities. This communication presents a generalised study of the SAG realisation with respect to the minimisation of the to0-sensitivity. A new canonic two operational amplifier network is proposed, and it is shown that according to the polarity of the VCVS in the circuil.s, two main classes of oscillators result with respect to the to0-sensitivity. A comparison finally ~ields the to0-insensitive SAG realisation with single grounded resistor control. 2. SAG realisation
The new SAG realisation scheme is shown in Fig. 1, where the triangle represents a VCVS of gain K that adjusts the oscillation maintenance condition. H represents the voltage transfer function (resistive) from terminal 1 to terminal 2 with respect to ground. The characteristic equation of the network is: (1- KH) 18
+
2a + 3(1 - K)
+l+a-K=0
.................
(1)
MICROELECTRONICS JOURNAL Vo115 No 3 ~ 1984 Benn Electronics Publications Ltd, Luton
_p r&
A:'
Fig. 1
T h e S A G network.
The maintenance condition and oscillation frequency (too) are as follows: K
= 1 + (--~--)
.................
(2)
.................
(3)
.
(4)
\-/
and,
too to~
where
to. .
a 3 - H(3 + 2a) .
1 .
.
.
.
;a>O
.
.
.
.
.
.
.
.
.
.
.
RC
Thus, choosing the quantity a arbitrarily, too can be independently controlled by a resistor of the resistive transfer block H. Depending on the design of the H block, as shown in Table I, two types of tuning for sub-audio generation may be obtained. Note that with non-inverting Table I Case
SAG realisation and sensitivity characteristics of the configuration of Fig. 1. H-block
ta...o0
Co0-sensitivity
too n
I Fig. 2(a)
V2 r2 H = -~-T = hi = rl + r2
II Fig. 2(b)
H = V4_ V4
III Fig. 2(c)
H = V_~6= _ ( 2 + h3) V,;
r2 rl
(1 - 3 hi) -v*
hz
- S c oc~o ~
r,
1/2
3hi(I-h1) (1-3hl)
(1 + 3 h2) - ~
S Coo__ _ sWO= V2 . r, r,
3 h2 (1+3 h2)
(7 + 3h3)_~h
- S C~ = S Coo= ~/~ r, r,
3h3 (7+3 h3)
h3 =rl/r 2 19
Desen~n of the oscillation frequency of RC sub-audio sinewave gec~r'ators with single resistor control continued from page 19
H (H = h 0 , a critical adjustment of the resistors (rt ~ 2 r2) yields very low-frequency generation; but with an inverting H block (H = - h2) no such critical adjustment is required and trimming the resistor rl to low values enables one to obtain continuously tunable sub-audio sinusoids. Thus the former technique, involving a difference term for to0-control, like the earlier circuits, 2s produces a concomitant increase in the to0-sensitivity, whereas in the later proposal too is practically insensitive in the desired sub-audio bands.
I o
V2.
rl
c
Vt
"r
~ vz t'2
A
V3
v4.
40
I v~
vS
rl
rt
v
i Fig. 2 Circuitimplementationof the SAG networks. 20
O
A grounded-resistor tunability of too is a desirable feature in view of the circuit's further application as a voltage-controlled oscillator (VCO). The grounded passive tuner resistor can be conveniently replaced by a voltage-variable resistor such as a field effect transistor operated below pinch-off. 8 To this end, the inverting H block implementation as in Fig. 2(c) would be appropriate in view of an insensitive voltage controlled SAG realisation. Here trimming of r2 to low values yields continuously tunable sub-audio sinusoids at extremely low sensitivities. Details of analytical observations on too and its sensitivity, with a = 3 for simplicity, are listed in Table I. Here the sensitivity figures are computed using the classical sensitivity definition s~ = (x/y) (Sy/Sx). It may be noted in the following table that in course of low-frequency generation in either case II(h2 > > 1) or case III (ha > > 1), the to0-sensitivities are quite low and are given by:
io01 iool Srl
=
St2
=
1/2
3. Experimental results The circuits proposed in Figs. 2(b) ~/nd (c) have been constructed in the laboratory using p,A741 operational amplifiers operating at ___12 volt regulated d.c. supply, and passive components with 10% tolerance. A typical design with hz = 100 has been verified experimentally and a good quality 5Hz sinusoid waveform was observed in the configuration of Fig. 2(b). The experimental waveform is shown in Fig. 3. Continuous tunability of oscillation frequency had been verified in both the configurations of Figs. 2(b) and (c). A frequency range without waveform distortion in Fig. 2(b) was obtained from 2Hz to about 20Hz, and, that in Fig. 2(c) was from 3Hz to 15Hz. The assumption of a very high-gain op-amp with high input impedance is sufficiently valid at these very low frequency ranges, and, amplifier nonidealities thus did not degrade the quality of the output waveform in the tuned band.
/ /ww Fig. 3
Experimentally obtained waveform of 5Hz in Fig. 2(b).
4. Conclusion Some investigations on the to0-sensitivities for a class of single resistor controlled SAG network configurations are presented. A novel method of desensitising the oscillation frequency (too) relative to the undesirable changes in the tuning components is described. A new canonic SAG circuit configuration scheme is proposed and its insensitive design has been worked out. Experimental results for a typical design are included. 21
~
n
of the oscillation frequency of I ~ sub~udio sinewave generatorswith single resistorcontrol
continued from page 21
5. Acknowledgment One of the authors (SN) is grateful to the Principal of Women's Polytechnic, Calcutta for support.
6.
References
[I'] Battye, C. K., "A low frequency selective amplifier", ]1. Sc. lnstrum., 34 (July 1957), pp. 263-265. [2] Shivaprasad, A. V., "A wide range variable frequency phase-shift oscillator", Trans. IEEE Instrum. Meas., IM-21 (May 1972), pp. 180-182. [3] Nandi, R., "New RC-oscillators with single-element controls", Int. ]1. Electron., 44 (Jan. 1978), pp. 65-78. [4] Ganguly, U. S., "RC-oscillator synthesis: Sub-audio frequency generation with single control", Proc. IEEE, 66 (April 1978), pp. 516-518. [5] Duttaroy, S. C. and Pyara, V. P., "Single element controlled oscillators: A network synthetic approach, Proc. IEEE, 67 (Nov. 1979), pp. 1565-1566. [6] Wilson, G., "Insensitive very low-frequency RC oscillator, Electronics Lett., 10 (Oct. 1974), pp. 447-448. [7] Nandi, R., "Integrable insensitive sub-audio frequency sinewave generator using DVCVS DVCCS", Proc. 1EEE, 67 (Nov. 1979), pp. 1568-1569. [8] Sundarmurthy, M., Bhattacharyya, B. B. and Swarny, M. N. S., "A simple voltage-controlled oscillator with grounded capacitors", Proc. 1EEE, 6.q (Nov. 1977), pp. 1612-1614. [9] Wilson, G., "An extremely low-capacitance very-low-frequency RC active network, Proc. IEEE, 64 (Nov. 1976), pp. 1626-1627.
22
Desensitisation of the oscillation frequency of RC sub-audio sinewave generators with single resistor control by A. R. Saha*, S. Nandi**, and R. Nandi* *Jadavpur University, India **Women's Polytechnic, Calcutta, India
This communication aims at treating the problem of desensitising the oscillation frequency (too) of a class of resistor-controlled sub-audio generator (SAG) on the basis of the examination of the t o o - s e n s ~ e s of such oscillators that are implemented through two main synthesis techniques. The study includes a new canonic SAG configuration realised with these techniques along with a comparison of their to0-sensitivities which finally derives the insensitive design.
1. Introduction Stable and insensitive realisation of low-frequency sinusoids at sub-audio bands finds applications in the measurement and test instrumentation of circuits and systems possessing relatively large time constants. In particular, sinewave generators covering 0.1 to 10 Hz are of interest for applications in geophysical, physiological and bioelectronic systems. 1 The synthesis of RC sub-audio generators (SAG) with single resistor control is receiving attention at present. 2s The general basis in all such synthesis techniques is to introduce some time constant enhancement factor by appropriate feedback in the network. Wilson 6,9 has shown that the use of low-pass positive feedback for a SAG realisation increases to0-sensitivities. This communication presents a generalised study of the SAG realisation with respect to the minimisation of the to0-sensitivity. A new canonic two operational amplifier network is proposed, and it is shown that according to the polarity of the VCVS in the circuil.s, two main classes of oscillators result with respect to the to0-sensitivity. A comparison finally ~ields the to0-insensitive SAG realisation with single grounded resistor control. 2. SAG realisation
The new SAG realisation scheme is shown in Fig. 1, where the triangle represents a VCVS of gain K that adjusts the oscillation maintenance condition. H represents the voltage transfer function (resistive) from terminal 1 to terminal 2 with respect to ground. The characteristic equation of the network is: (1- KH) 18
+
2a + 3(1 - K)
+l+a-K=0
.................
(1)
MICROELECTRONICS JOURNAL Vo115 No 3 ~ 1984 Benn Electronics Publications Ltd, Luton
_p r&
A:'
Fig. 1
T h e S A G network.
The maintenance condition and oscillation frequency (too) are as follows: K
= 1 + (--~--)
.................
(2)
.................
(3)
.
(4)
\-/
and,
too to~
where
to. .
a 3 - H(3 + 2a) .
1 .
.
.
.
;a>O
.
.
.
.
.
.
.
.
.
.
.
RC
Thus, choosing the quantity a arbitrarily, too can be independently controlled by a resistor of the resistive transfer block H. Depending on the design of the H block, as shown in Table I, two types of tuning for sub-audio generation may be obtained. Note that with non-inverting Table I Case
SAG realisation and sensitivity characteristics of the configuration of Fig. 1. H-block
ta...o0
Co0-sensitivity
too n
I Fig. 2(a)
V2 r2 H = -~-T = hi = rl + r2
II Fig. 2(b)
H = V4_ V4
III Fig. 2(c)
H = V_~6= _ ( 2 + h3) V,;
r2 rl
(1 - 3 hi) -v*
hz
- S c oc~o ~
r,
1/2
3hi(I-h1) (1-3hl)
(1 + 3 h2) - ~
S Coo__ _ sWO= V2 . r, r,
3 h2 (1+3 h2)
(7 + 3h3)_~h
- S C~ = S Coo= ~/~ r, r,
3h3 (7+3 h3)
h3 =rl/r 2 19
Desen~n of the oscillation frequency of RC sub-audio sinewave gec~r'ators with single resistor control continued from page 19
H (H = h 0 , a critical adjustment of the resistors (rt ~ 2 r2) yields very low-frequency generation; but with an inverting H block (H = - h2) no such critical adjustment is required and trimming the resistor rl to low values enables one to obtain continuously tunable sub-audio sinusoids. Thus the former technique, involving a difference term for to0-control, like the earlier circuits, 2s produces a concomitant increase in the to0-sensitivity, whereas in the later proposal too is practically insensitive in the desired sub-audio bands.
I o
V2.
rl
c
Vt
"r
~ vz t'2
A
V3
v4.
40
I v~
vS
rl
rt
v
i Fig. 2 Circuitimplementationof the SAG networks. 20
O
A grounded-resistor tunability of too is a desirable feature in view of the circuit's further application as a voltage-controlled oscillator (VCO). The grounded passive tuner resistor can be conveniently replaced by a voltage-variable resistor such as a field effect transistor operated below pinch-off. 8 To this end, the inverting H block implementation as in Fig. 2(c) would be appropriate in view of an insensitive voltage controlled SAG realisation. Here trimming of r2 to low values yields continuously tunable sub-audio sinusoids at extremely low sensitivities. Details of analytical observations on too and its sensitivity, with a = 3 for simplicity, are listed in Table I. Here the sensitivity figures are computed using the classical sensitivity definition s~ = (x/y) (Sy/Sx). It may be noted in the following table that in course of low-frequency generation in either case II(h2 > > 1) or case III (ha > > 1), the to0-sensitivities are quite low and are given by:
io01 iool Srl
=
St2
=
1/2
3. Experimental results The circuits proposed in Figs. 2(b) ~/nd (c) have been constructed in the laboratory using p,A741 operational amplifiers operating at ___12 volt regulated d.c. supply, and passive components with 10% tolerance. A typical design with hz = 100 has been verified experimentally and a good quality 5Hz sinusoid waveform was observed in the configuration of Fig. 2(b). The experimental waveform is shown in Fig. 3. Continuous tunability of oscillation frequency had been verified in both the configurations of Figs. 2(b) and (c). A frequency range without waveform distortion in Fig. 2(b) was obtained from 2Hz to about 20Hz, and, that in Fig. 2(c) was from 3Hz to 15Hz. The assumption of a very high-gain op-amp with high input impedance is sufficiently valid at these very low frequency ranges, and, amplifier nonidealities thus did not degrade the quality of the output waveform in the tuned band.
/ /ww Fig. 3
Experimentally obtained waveform of 5Hz in Fig. 2(b).
4. Conclusion Some investigations on the to0-sensitivities for a class of single resistor controlled SAG network configurations are presented. A novel method of desensitising the oscillation frequency (too) relative to the undesirable changes in the tuning components is described. A new canonic SAG circuit configuration scheme is proposed and its insensitive design has been worked out. Experimental results for a typical design are included. 21
~
n
of the oscillation frequency of I ~ sub~udio sinewave generatorswith single resistorcontrol
continued from page 21
5. Acknowledgment One of the authors (SN) is grateful to the Principal of Women's Polytechnic, Calcutta for support.
6.
References
[I'] Battye, C. K., "A low frequency selective amplifier", ]1. Sc. lnstrum., 34 (July 1957), pp. 263-265. [2] Shivaprasad, A. V., "A wide range variable frequency phase-shift oscillator", Trans. IEEE Instrum. Meas., IM-21 (May 1972), pp. 180-182. [3] Nandi, R., "New RC-oscillators with single-element controls", Int. ]1. Electron., 44 (Jan. 1978), pp. 65-78. [4] Ganguly, U. S., "RC-oscillator synthesis: Sub-audio frequency generation with single control", Proc. IEEE, 66 (April 1978), pp. 516-518. [5] Duttaroy, S. C. and Pyara, V. P., "Single element controlled oscillators: A network synthetic approach, Proc. IEEE, 67 (Nov. 1979), pp. 1565-1566. [6] Wilson, G., "Insensitive very low-frequency RC oscillator, Electronics Lett., 10 (Oct. 1974), pp. 447-448. [7] Nandi, R., "Integrable insensitive sub-audio frequency sinewave generator using DVCVS DVCCS", Proc. 1EEE, 67 (Nov. 1979), pp. 1568-1569. [8] Sundarmurthy, M., Bhattacharyya, B. B. and Swarny, M. N. S., "A simple voltage-controlled oscillator with grounded capacitors", Proc. 1EEE, 6.q (Nov. 1977), pp. 1612-1614. [9] Wilson, G., "An extremely low-capacitance very-low-frequency RC active network, Proc. IEEE, 64 (Nov. 1976), pp. 1626-1627.
22