OTA-Based Triangular-to-Sine and Sine-to-Triangular
Waveform Converters
Anucha Kaewpoonsuk1, Sutthinon Khunkong1, Apinai Rerkratn2, Wandee Petchmaneelumka2,
and Naratorn Kanjanapart2
1
2
Department of Physics, Naresuan University, Phitsanulok 65000, Thailand
Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang,
Chalongkrung Rd, Ladkrabang, Bangkok, 10520, Thailand
Abstract
An alternative technique for realizing both triangular-to-sine waveform converter and its inverse transfer function based
on operational transconductance amplifier (OTA), are presented in this paper. The proposed waveform converting action is
exploited from the hyperbolic tangent characteristic of bipolar junction transistor-based (BJT-based) OTA. The proposed
schemes provide the simple configulation and employ only OTAs as the active elements. PSPICE simulation and
experimental results are given to confirm the theoretical analysis.
Keywords - OTA, Triangular-to-sine waveform converter, Sine-to-triangular waveform converter
1
Introduction
Triangular-to-sine waveform converter and its inverse transfer
function, which is sine-to-triangular waveform converter, are
important circuit building blocks in electronic signal processing.
Three fundamental approaches for determining both waveform
converters are based on the diode-network [1], the differential
pair-network [2], and the translinear circuit [3]. It has been
demonstrated that the OTA, which is implemented by bipolar
junction transistors (BJTs), can be used to implement a sine-totriangular waveform converter [4-5]. However, that circuit
requires four OTAs for conversion waveform signal. If the
number of OTAs can be minimized, the approach will provide
the economical attraction. Therefore, the purpose of this article
is to propose a new topology both triangular-to-sine and sine-totriangular waveform converters based on OTAs. Moreover, the
circuits provide a simple configuration and require only OTA as
active element.
2
The circuit schematic diagram and the symbol of BJT-based
OTA is shown in Fig. 1, where Vin, Iout and IB denote the input
voltage, output current, and the bias current of OTA,
respectively. Transistors Q1-Q2 function the differential pair. All
current mirrors (CMi), where i = 1, 2 and 3, is assigned to unity
current gain, the relation between the Vin and the Iout can be
stated as
I out  I B tanh(Vin / 2VT )
(1)
Vin  2VT tanh 1 ( I out / I B )
(2)
where VT is the thermal voltage.
(4)
Vin  ( 2VT  I B R ) sin 1 (mI o / I B )
or
(5)
I o  ( I B / m) sin(Vin /(2VT  I B R))
CM1
CM3
Iout
Vin
Circuit Description
Q1 Q2
IB
CM2
(a) Circuit schematic diagram.
(b) Symbol
The realization of proposed triangular-to-sine waveform
converter utilizing hyperbolic tangent behavior of OTA is
shown in Fig. 2. Thus, the relation between the input signal Vin
and the current signal Io can be express as
Vin  I o R  2VT tanh 1 ( I o / I B )
Based on the power series expansion principles and using
suitable conditions such as (IBR / 2VT) = 1.3, and the magnitude
(m) of the current Io is set to m = 0.975IB, Eq. (3) can be
approximated as
(3)
Fig. 1. BJT-based OTA.
Then the output voltage signal Vout can be written as
Vout  R ( I B / m) sin(Vin /(2VT  I B R))
(6)
Clearly, the proposed circuit can exhibit as a triangular-to-sine
waveform converter.
Fig. 3 shows the proposed sine-to-triangular waveform
converter, which consists of a resistor R and two BJT-based
OTAs. OTA1 and resistor R function as a triangular-to-sine
waveform converter. The OTA2 is used as a feedback of the
proposed circuit. Hence the relationship of the input signal Vin
and the output signal Vout can be approximated by
Vout  (2VT  I B R) sin 1 (mVin / I B R)
(7)
From Eq. (7), if Vin is the sinusoidal waveform then we get the
output signal Vout as a triangular waveform.
3
PSPICE Simulation Results
To demonstrate the circuit performances of the proposed
triangular-to-sine and sine-to-triangular waveform converters,
the schemes in Figs. 2~3 were simulated using PSPICE analog
simulation program. The simulation results were carried out
using the commercial OTA model. The circuit parameters R =
1kΩ, IB = IB1 = 67uA and IB2 = 500uA were chosen. The supply
voltages of all circuits were set to ±15V.
Figs. 5~6 show simulation results of the proposed circuits in
Figs. 2~3. From Fig. 5, the input voltage Vin is 1kHz triangular
signal with 380mVp-p. From Fig.6, the input voltage Vin is 1kHz
sinusoidal waveform with 150mVp-p. It is evident that the
simulation results of the proposed circuits are in close
agreement with the expected values.
Fig. 2. Proposed triangular-to-sine waveform converter.
Fig. 5. Simulated results of proposed triangular-to-sine waveform
converter.
Fig. 3. Proposed sine-to-triangular waveform converter.
From triangular-to-sine and sine-to-triangular waveform
converters as shown in Figs. 2~3, the alternative schemes for
out-of-phase waveform results can be shown in Fig. 4.
(a) Triangular-to-sine
Fig. 6. Simulated results of proposed sine-to-triangular waveform
converter.
(b) Sine-to-triangular
Fig. 4. Alternative converters for out-of-phase waveform results.
The schemes in Fig. 4 was simulated using PSPICE analog
simulation program. The simulation results were carried out
using the commercial OTA model. The circuit parameters R1 =
10kΩ, R2 = 10kΩ IB1 = 67uA and IB2 = 500uA were chosen. The
supply voltages of all circuits were set to ±15V.
Figs.7~8 show simulation results of the proposed circuits in
Fig. 4. From Fig. 7, the input voltage Vin is 1kHz triangular
waveform with 380mVp-p. From Fig. 8, the input voltage Vin is
1kHz sinusoidal waveform with 150mVp-p.
Vin (mV)
Vin, Vout (mV)
200
0
Vin
Vout
Vout (expected)
-200
Vout (mV)
Error (%FS)
4
0
-4
-90
0
Phase (degree)
90
Fig. 10. Simulated error of proposed sine-to-triangular waveform
converter.
Fig. 7. Simulated results of out-of-phase triangular-to-sine waveform
converter.
4
Experimental Results
Vout (mV)
Vin (mV)
The proposed triangular-to-sine and sine-to-triangular
waveform converters in Figs. 2~3 were experimental implemented
using commercial available OTA CA3280 and 1% tolerance
resistor. The circuit parameters R = 1kΩ, IB = IB1 = 200uA and IB2
= 100uA were chosen. The supply voltages of all circuits were set
to ±15V. Figs.11~12 show experimental results of the proposed
circuits in Figs. 2~3, respectively. From Fig. 11, the input voltage
Vin is 1kHz triangular with 400mVp-p. From Fig.12, the input
voltage Vin is 1kHz sinusoidal with 400mVp-p.
Fig. 8. Simulation results of out-of-phase sine-to-triangular waveform
converter.
200
100
Fig. 11. Experimental results of proposed triangular-to-sine waveform
converter.
0
100
50
0
2.5
5
Frequency (kHz)
7.5
10
Fig. 9. Simulated frequency spectrum of proposed triangular-to-sine
waveform converter.
Fig. 9 shows simulated frequency spectrum of the proposed
triangular-to-sine waveform converter in Fig. 2. Fig. 10 shows
simulated error of proposed sine-to-triangular waveform
converter in Fig. 3. The maximum error is about 3 percentages.
From the simulated results in Figs. 5~10, it is evident that the
proposed converters performance are agreed with the expected
values.
Fig. 12. Experimental results of proposed sine-to-triangular waveform
converter.
The proposed triangular-to-sine and sine-to-triangular
waveform converters in Fig. 4(a) ~ 4(b) were experimental
implemented using commercial available OTA CA3280 and 1%
tolerance resistor. The circuit parameters R1 = 10kΩ, R2 = 10kΩ,
IB1 = 67uA and IB2 = 500uA were chosen. The supply voltages of
all circuits were set to ±15V. Figs.13~14 show experimental
results of the proposed circuits in Figs. 4(a) ~ 4(b), respectively.
From Fig.13, the input voltage Vin is 1kHz triangular waveform
400mVp-p. From Fig.14, the input voltage Vin is kHz sinusoidal
signal 400mVp-p. It is clearly seen that the experimental results of
the proposed circuits are in close agreement with the expected
values.
Fig. 13. Experimental results of out-of-phase triangular-to-sine
waveform converter.
Fig. 14. Experimental results of out-of-phase sine-to-triangular
waveform converter.
5
Conclusion
In this paper, triangular-to-sine and sine-to-triangular
waveform converters has been described. The proposed circuits
provide simple configuration, good performance and low cost.
Simulation and experimental results verifying the performance
of the proposed circuit are agreed with the expected values.
References
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Discrete”, Delmar, a division of Thomson Learning, Inc. USA, pp.
525-526, 2002.
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Differential Pair as a Triangle-Sine WaveConverter,” IEEE Journal
of Solid-State Circuits, SC-11, pp:418-420, June 1976.
[3] B. Gilbert, “A Monolithic Mycrosystem for Analog Synthesis of
Trigonometric Functions and Their Inverses,” IEEE Journal of
Solid-State Circuits, SC-17, No.6, pp:1179-1191, December 1982.
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Processing, December 2006, Volume 25, Issue 6, pp 753-765
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.