วารสารวิชาการพระจอมเกล้าพระนครเหนือ ปีท่ี 12 ฉบับที่ 3 ก.ค. - ก.ย. 2545
The Journal of KMITNB., Vol. 12, No. 3, Jul. - Sep. 2002
Differentiated Input and Frequency-Constant PWM Signal Generation
Scheme Based on Novel Schmitt Trigger
Montree Siripruchyanun*
proposed the simple PWM signal generator [2-5],
Abstract
the scheme details do have frequency of PWM
This article presents a novel Schmitt trigger
arising from
output signal dependent on amplitude of modulating
differentiation of modulating input signal in the
signal. This makes them can not be applied in
provided time. The outstanding feature of the
the case of adjacent of modulating
proposed scheme is that the PWM output has
and carrier frequency, so the carrier frequency is
frequency-constant which does not depend on
provided to be a much higher than ten times of
amplitude of modulating signal. That makes it
the modulating frequency [6-7]. In addition, some
suitable to use in application of adjacent frequency
above proposed methods, their duty cycle of PWM
between
output signal does not linearly vary with modulating
that
can
differs
originate PWM signal
carrier
from
the
and modulating signal, which
conventional
PWM
frequency
signal which causes it has some distortion after
signal
demodulation.
generators. Furthermore, the proposed circuit has
relatively simpler scheme. It consists of merely
The purpose of this article is to present an
3 OTAs, 2 resistors and 1 grounded capacitor,
innovation of PWM signal generation. The features
thus it is suitable for both circuit implementation
are that not only the frequency of PWM output
and IC realization. The experimental results are
signal is independent of modulating signal, but also
shown which is in correspondence to theoretical
the PWM signal is originated from differentiating of
anticipation.
the modulating signal that makes it has relatively
higher signal to noise ratio (S/N) than the previous
methods. Furthermore, the circuit description of PWM
1. Introduction
Pulse Width Modulation (PWM) signal is widely
signal generation based on novel Schmitt trigger [8]
utilized in the areas of communication, especially in
is simple, because of integrating triangular wave
optical communication and instrumentation. By the
generator, signal adder and comparator into same
reason, the PWM signal generator has been realized
circuit. The proposed PWM signal generation can
in Integrated Circuits (ICs) form that makes it
provide precise PWM signal even adjacent of
convenient to implement. However, the circuit
carrier and modulating frequency is related. The
configuration is typically composed of current sources,
experimental results demonstrated can insist on
flip-flop, comparators and analog switches as well
high performance of the proposed PWM signal
[1]. Although, the recently previous literatures have
generation method.
*
Department of Teacher Training in Electrical Engineering, Faculty of Technical Education,
King Mongkut’s Institute of Technology North Bangkok.
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วารสารวิชาการพระจอมเกล้าพระนครเหนือ ปีท่ี 12 ฉบับที่ 3 ก.ค. - ก.ย. 2545
The Journal of KMITNB., Vol. 12, No. 3, Jul. - Sep. 2002
Modulating
Input
2. Principle
2.1 The Conventional PWM Signal Generation
∑
Comparator
Output
Signal
The conventional PWM signal used in
communication systems is schematically depicted in
Triangular Wave
Generator
Fig. 1 [9-12]. If we assume that sinusoidal signal
is modulating (information) signal, the amplitude
Reference Level
summation of the modulating signal and triangular
carrier wave is illustrated in the middle line of
Fig. 1 The PWM signal generation in communication
Fig. 2. Then PWM signal output signal is generated
systems
by comparing the summation result and reference
level demonstrated in bottom line of Fig. 2. We can
Modulating
Signal
found that although carrier frequency is not much
higher than information frequency, the PWM output
The summation of
modulating signal
and carrier signal
Reference
level
frequency is rather not constant. So in typical
applications, the carreir frequency is provided to be
PWM
output
much higher than ten times of the information
frequency [6-7].
T 1 T2
2.2 Principle of Proposed PWM Signal Generation
The PWM signal generation which comes
from differentiated result of modulating signal has
Fig. 2 The signals in PWM signal generation of Fig.1
scheme shown in Fig. 3. Its principle is that
finding differential result of modulating signal
vi (t )
during t1 and t2 which are switched times of
carrier voltage to change its polarity. The duty
cycle ( D ) is then dependent on differential result
Differential
of
Modulating
Signal
PWM output
PWM
of modulating signal at t1 and t2 (see Fig.5)
which can be controlled by carrier frequency
Sampling Time
following eqn. (1).
Fig. 3 Principle of proposed PWM signal generation
D = 1 [ 1 + k∆ υ i (t) ]
2
x 100%
(1)
It is clearly seen that, from eqn. (2), the duty cycle
Where k is circuit constant value and
of PWM signal is dependent on differentiated result
∆ υ i (t) = υ i (t 2) - υ i (t 1). We can see that, from eqn.
of the information signal. We can anticipate that
(1), if ∆ υ i (t) = 0 this means that no variation
if common mode noise involves in the modulating
of modulating signal, the duty cycle will be 50%.
signal, the noise can be eliminated because only
In the case of the carrier frequency is much
differential result of modulating signal is transformed
greater than the modulating frequency, we can
to be pulse width of output signal whereas the
assume that
output frequency is constant. The exact information
signal can be achieved by using integrator circuit
∆ υ i (t) = dυ i(t)
(2)
after demodulation.
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วารสารวิชาการพระจอมเกล้าพระนครเหนือ ปีท่ี 12 ฉบับที่ 3 ก.ค. - ก.ย. 2545
The Journal of KMITNB., Vol. 12, No. 3, Jul. - Sep. 2002
vo1 (t )
2.3 Schematic Description
The proposed scheme is illustrated in Fig. 4
IB3R1
whereas υ i (t) is the modulating signal, which is firstly
connected to ground for easily understanding the
circuit. From the circuit, OTA1 and the timing
t
0
capacitor C function as an integrator whose time
constant is proportional to the bias current IB1. The
−IB3R1
OTA2, OTA3 and the resistors R1 and R2 work as a
Schmitt trigger whose threshold voltage is proportional
vo2 (t )
to the bias current IB3 and saturation voltage is
proportional to the bias current IB2. Then the
IB2 R2
waveforms generated from the proposed circuit;
υ o1(t) and υ o2(t) will respectively be triangular and
t1
square wave as Fig. 5.
T1
t2
t
0
In theoretical derivation, it is easy to display
that time interval of positive saturation voltage and
T2
that of negative saturation voltage are respectively
−IB2R2
indicated as
T
T1 =
2RCI B3
I B1
(3)
T2 =
2RCI B3
I B1
(4)
Fig. 5 Signals in the proposed circuit
Then we get the period time and frequency of
carrier oscillation respectively as
IIB1
B1
++
11
-
υvoo11((t)
t)
C
C
4R 1CI B3
I B1
f =
1
4R1C
(5)
( )
I B1
I B3
(6)
The expression of triangular wave and square
υv
(t)
o2o2(t)
-+
22
+
T=
wave amplitude are respectively given by
υ o1(p - p) =
2I B3 R 1
(7)
υ o2(p - p) =
2I B2 R 2
(8)
I
IBB22
++
33
υvo3o3(t)
(t)
The relationship between eqn. (6), (7) and (8) shows
-
R11
IIBB33
that its frequency and amplitude can be independently
R22
tunable. It means that the carrier oscillation frequency
can be adjusted by I B1, the triangular wave amplitude
υvii(t)
(t)
adjustment can be done by I B3 and the square wave
Fig. 4 The circuit diagram of proposed scheme
amplitude can be tuned by I B2.
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วารสารวิชาการพระจอมเกล้าพระนครเหนือ ปีท่ี 12 ฉบับที่ 3 ก.ค. - ก.ย. 2545
The Journal of KMITNB., Vol. 12, No. 3, Jul. - Sep. 2002
In addition, it should be observed that the
oscillation frequency is independent of power supply
voltage and temperature because of compensation of
current ratio I B1/I B3.
If υ i (t) is assumed as a modulating (information)
signal, time intervals of
positive and negative
saturation voltage of υ o2(t) depend on the modulating
signal respectively shown as
T1 =
T2 =
2R 1 CI B3
IB 1
2R 1 CI B3
[
[
1+
1+
υ i(t 2 ) − υ i(t 1 )
2I B3 R 1
υ i(t 1 ) − υ i(t 2 )
]
]
(9)
Fig. 7 Frequency spectrum of PWM output signal
of 16 kHz carrier frequency and modulating
(10)
signal as sinewave with 1kHz frequency,
amplitude of 1V
We found that the period time of oscillation (carrier)
which comes from summation of T1 and T2 is equal to
eqn. (5), hence the oscillation frequency still be
equal to eqn. (6) while its duty cycle depends on the
differential result of modulating signal as following
D =
1
2
(
1+
∆ υ i (t)
2IB3R1
)
x 100%
(11)
where ∆ υ i (t) is derivative of the modulating voltage
( υ i (t 2 ) - υ i (t 1 )). If the circuit has condition as eqn.
(a)
(2), it demonstrates that the proposed scheme can
function as the differentiated PWM signal generator.
The features are, independency of frequency against
the modulating signal variation, and the relatively
simple scheme due to integration of various stages
of PWM signal generator such as triangular wave
generator, adder and comparator into the same circuit.
The accurate modulating signal can be recovered by
using integrator circuit after demodulation of the
PWM signal.
(b)
3. Experimental Results and Discussions
Fig. 6 The results with upper trace is modulating
The proposed circuit was experimentally tested
signal and lower trace is PWM output signal
using the CA3080 OTAs. The results are obtained
whereas carrier frequency of (a) 5kHz (b) 20kHz
with resistor 10kΩ and capacitor 1nF operating with
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วารสารวิชาการพระจอมเกล้าพระนครเหนือ ปีท่ี 12 ฉบับที่ 3 ก.ค. - ก.ย. 2545
The Journal of KMITNB., Vol. 12, No. 3, Jul. - Sep. 2002
±5V supply. The first experimental results were set up
with 1.5kHz
cut-off
frequency to achieve the
with modulating signal of sine wave with frequency of
information signal. In this experiments, the carrier
5kHz and 20kHz. These results are shown in Fig. 6(a)
frequency is set to be 50kHz and modulating
and (b) respectively, it can be clearly seen that the
frequency of 300Hz for triangular and square wave.
frequency of PWM output signal is independent of
The results respectively shown in Fig. 8(a) and (b),
the magnitude of modulating signal.
it is clearly seen that the recovered signals are
The result of frequency spectrum with carrier
differentiated results of the information signal, which
frequency of 16kHz and the same modulating signal
can be transformed to achieve exact information
is also demonstrated in Fig. 7. It is found that it
signal by using an integrator circuit.
consists of modulating signal component, so it can
be recovered by using a low pass filter [13]. It is
4. Conclusions
nd
proved by utilizing 2 order active low pass filter
The
innovation
of
simple
PWM signal
generation of differentiated result of information
signal has been reported. The features of proposed
scheme are that, the frequency of PWM output
signal is independent of magnitude of information
signal which differs from conventional PWM signal
generation, it can generate a precise PWM signal
even adjacent of carrier frequency and modulating
frequency is involved. In addition, with the proposed
circuit, its carrier frequency and amplitude can
be electronically adjusted
with insensitivity of
temperature and power supply voltage. It also utilizes
low cost commercial devices over a wide range of
(a)
frequency.
5. Acknowledgement
The Author would like to thank Associate
Professor Dr. Paramote Wardkein, Department of
Telecommunication
Engineering,
Faculty
of
Engineering, King Mongkut’s Institute of Technology
Ladkrabang
for
his
valuable suggestions and
discussions.
References
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(b)
APEX Microtechnology, “PWM Basics, Pulse
Width Modulator Amplifier.” Application Note
30.
Fig. 8 The results of information recovery from PWM
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signal at 50kHz frequency and modulation
Amplifiers Third-Generation Techniques.
signal as (a) triangular wave (b) square wave
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วารสารวิชาการพระจอมเกล้าพระนครเหนือ ปีท่ี 12 ฉบับที่ 3 ก.ค. - ก.ย. 2545
The Journal of KMITNB., Vol. 12, No. 3, Jul. - Sep. 2002
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Engineering