Circuits and Systems, 2013, 4, 287-292
http://dx.doi.org/10.4236/cs.2013.43039 Published Online July 2013 (http://www.scirp.org/journal/cs)
A Synthesis of Electronically Controllable Current-Mode
PI, PD and PID Controllers Employing CCCDBAs
Somchai Srisakultiew1,2, Montree Siripruchyanun2*
1Department of Computer Engineering, Faculty of Engineering and Architecture, Rajamangala University of
Technology Isan, Nakhonratsima, Thailand
2Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of
Technology North Bangkok, Bangkok, Thailand
Received March 21, 2013; revised April 30, 2013; accepted May 7, 2013
Copyright © 2013 Somchai Srisakultiew, Montree Siripruchyanun. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original
work is properly cited.
ABSTRACT
This paper presents a synthesis of current-mode PI, PD and PID controllers employing current controlled current dif-
ferential buffer amplifiers (CCCDBAs). The features of these controllers are that: the output parameters can be elec-
tronically/independently controlled by adjusting corresponding bias currents in the proportional, integral, and deviation
controllers; circuit description of the PID controller is simply formulated, it consists of four CCCDBAs cooperating
with two grounded capacitors, and PI and PD controllers are composed of three CCCCDBAs and a grounded capacitor.
Without any external resistor, the proposed circuits are very suitable to develop into integrated circuit architecture. The
given results from the PSpice simulation agree well with the theoretical anticipation. The approximate power consump-
tion in a closed loop control system consisting of the PI, PD and PID controller with low-pass filter passive plant are
4.03 mW, 4.85 mW and 5.71 mW, respectively, at ±1.5 V power supply voltages.
Keywords: Current-Mode; PID Controller; CCCDBA
1. Introduction
The proportional-integral-derivative (PID) controllers are
the most important control devices employed in indus-
trial process control [1]. Classical implementations of the
PID controller contain several active elements to realize
the transfer function. For instance, parallel structure us-
ing operational amplifiers (Op-Amp) [2] requires four
sections: Proportional (P), Integral (I), Derivative (D)
transfers and adder. Proportional-integral (PI), Propor-
tional-derivative (PD) and PID controllers with adjust-
able parameters are implemented in various pieces of
work. These controllers are used in many applications,
for example, motor speed controllers, temperature con-
trollers, fluid controllers and etc. [3,4].
For the last two decades, the attention is subsequently
focused on the PID controllers using different high-per-
formance active building blocks such as, operational
transconductance amplifiers (OTAs) [5,6], current feed-
back op-amp (CFAs) [7,8], second generation current
conveyors (CCIIs) [9-13], second generation current
controlled current conveyors (CCCIIs) [14-16], and cur-
rent differencing buffered amplifiers (CDBAs) [17]. The
literature surveys show that a large number of circuit
realizations for PI, PD and PID controllers simulators
have been reported [5-17]. Unfortunately, these reported
circuits suffer from one or more of following weak-
nesses:
 Excessive use of the active and/or passive elements
[5-17];
 Circuit requirement external resistors [5,6,7-17];
 Lack of electronic tenability [7-13,17];
 Absence of independent control of their parameters
[5,7,9,14,15].
The current differencing buffered amplifier (CDBA) is
a reported active component especially suitable for a
class of analog signal processing [18]. The fact that the
device which can operate in both current and voltage
modes provides flexibility and enables a variety of circuit
designs. In addition, it can offer advantageous features
such as high-slew rate, free from parasitic capacitances,
wide bandwidth and simple implementation [19]. How-
ever, the CDBA cannot be controlled by the parasitic
*Corresponding author.
C
opyright © 2013 SciRes. CS

S. SRISAKULTIEW, M. SIRIPRUCHYANUN 288
resistances at two current input ports so when it is used in
a circuit, it must unavoidably require some external pas-
sive components, especially the resistors. This makes it
not appropriate for IC implementation due to occupying
more chip area, higher power dissipation and cannot
electronic controllable. Subsequently, Maheshwari and
Khan have proposed the modified-version CDBA whose
parasitic resistances at two current input ports can be
controlled by an input bias current and it is newly named
current controlled current differencing buffered amplifier
(CCCDBA) [20].
Presently, a current-mode technique has been more
popular than the voltage-mode one. This is due to oper-
ating in the low-voltage environment found portable and
battery-powered equipment. Since a low-voltage operat-
ing circuit has become necessary, the current-mode tech-
nique is ideally suited for this purpose more than the
voltage-mode one. Furthermore, there is a growing inter-
est in synthesizing the current-mode circuits because of
their unique potential advantages such as larger dynamic
range, higher signal bandwidth, greater linearity, simpler
circuitry, and lower power consumption [21].
The purpose of this paper is to introduce a synthesis of
current-mode PI, PD and PID controllers employing
CCCDBAs. The features of the proposed controllers are
that: the output parameter can be electronically/inde-
pendently controlled by adjusting corresponding bias
currents in the proportional, integral, and deviation con-
trollers: circuit description of the PID controller is very
simple, consisting of four CCCDBAs cooperating with
two grounded capacitors. PI and PD controller consists of
three CCCDBAs cooperating with a grounded capacitor.
The simulations are performed by PSpice to exhibit the
performance of the developed controllers.
2. Theory and Principle
2.1. Basic Concept of Current Controlled
Current Differencing Buffered Amplifier
(CCCDBA)
Since the proposed circuits are based on CCCDBAs, a
brief review of CCCDBA is given in this section. Basi-
cally, the CCCDBA is composed of translinear elements,
mixed loops and complementary current mirrors. Gener-
ally, its properties are similar to the conventional CDBA
[19], except that input voltages of CCCDBA are not zero
and the CCCDBA has finite input resistances Rp and Rn
at the p and n input terminals, respectively. These intrin-
sic resistances are equal and can be controlled by the bias
current IB as shown in the following equation
1, 211
00
p
n
zz
R
R


 

 



For BJT CCCDBA, the input resistances; Rp and Rn
can be expressed to be
000
000
,
00
10
pp
nn
z
ww
VI
VI
IV
VI






 
 


(1)
.
2
T
pn
V
RR (2)
I

B
VT and IB are the thermal voltage and input bias current,
respectively. The symbol and the equivalent circuit of the
CCCDBA are illustrated in Figures 1(a) and (b), respec-
tively.
2.2. Synthesis of Proposed Controllers
Employing CCCDBAs
2.2.1. P I C ontroller
PI controller is composed of a proportional and an inte-
gral term. The PI controller is sufficient when the process
dynamics is an essentially first-order system. The pro-
posed PI controller employs three CCCDBAs, a grounded
capacitor as shown in Figure 2. Transfer function of
general PI controller:


H
PI s

can be written as (3).
PI
1
OPi
in i
I
HsK .
I
Ts
  (3)
I
B
p
n
w
1
z
2
z
I
p
I
I
z
1 n
I
z
2
(a)
p
I
p
R
n
n
I
R
n
p
w
V
12
1wz
VV
1
I
I
z
2
z
z
zpn
I
III
1
z


2
z
(b)
Figure 1. The CCCDBA (a) symbol (b) equivalent circuit.
Figure 2. The proposed PI controller.

S. SRISAKULTIEW, M. SIRIPRUCHYANUN 289
The CC 2 has the
tra
CDBA based PI controller in Figure
nsfer function as

2
1
.
2
On B
B
PI
in
I
CR I
Hs
I
Is
 (4)
g

Substitutin 2 T
n
V
R into (4), it yields
I
B

PI
O
in
I2
13
2.
2
BT
B B
I
VC
IIsI
 (5)
From (5), it is found that HPI and T can be independ-
en
Hs
i
tly controlled by 12
B
B
I
I and IB3, respectively.
Figure 3. The proposed PD controller.
2.2.2. PD Controller
e most widely used in strategy for The PD controller is th
robot manipulators, motor speed control, and etc. Addi-
tionally, more advanced controllers often incorporate to
PD algorithms in their control-loop to reach the desired
configuration. The derivative term of the PD controller
deals with slope of error, and it is effective in the tran-
sient-response. The derivative term has no effect if the
steady-state error is constant in a corresponding time.
The proposed PD controller employs three CCCDBAs,
one grounded capacitor shown in Figure 3. The general
transfer function of PD controller:

PD
H
scan be writ-
ten in (6)

PD
O
in
I.
Pd d
H
sKTs (6)
The CCCDBAs based PD controller shown in Figure
3
I
has the transfer function as (7)

2
1
.
2
Bn
B
PD
O
in
II
H
sRsC
II
  (7)
g Substitutin2 T
n
B
V
R
I
into (7), it yields

2
13
.
22
BT
B B
PD
O
in
I
I
VsC
Hs
I
II
 (8)
From (8), it can be seen that the KP can be electroni-
ca
2.2.3. PID Controlle r
rivative (PID) controllers are ex-
mode PID controller is shown in
Fi

lly controlled by either IB1 or IB2 and TD parameter can
be adjusted by adjust IB3 with independent each other.
Proportional-integral-de
tensively used in industry. It is estimated that more than
90% of all control loops involve PID controllers, where
the proportional term adjusts the speed response of the
system, the integral term adjusts the steady-state error of
the system and the derivative term adjusts the degree of
stability of the system.
The proposed current-
gure 4. It consists of only four CCCDBAs and two
p
n
z
CCCDBA1
IB3
p
n
z2
CCCDBA3
Iin
c1
IB1 IB2
p
n
z
CCCDBA2
w
Io
z1
IB4
p
n
z
CCCDBA4
Current
Splitter
c2
Figure 4. The proposed PID controller.
rounded capacitors. The transfer function of general g
analog PID controller:

PID
H
scan be written as de-
picted in (9), where Kp isportional gain, Ki is the
integral time, and Kd is the derivative time parameters
the pro





PID
2
PID
,
.
out i
p
d
in
dpi
Is K
H
sKsK
Is s
KsKs K
Hs s



(9)
The transfer function of the proposed PID controller
w

ill be shown by
24 2
PID1 3
1
.
2
On Bn
in B
ICR
I
H
ssCR
II s
  (10)
Substituting 2 T
ni
B
i
V
R
I
into (10), we obtain

22
PID
143
.
222
OBTT
in BBB
I
I
VC VsC
Hs
I
IsI I
  (11)

S. SRISAKULTIEW, M. SIRIPRUCHYANUN 290
From (11), the PID controller’s parameters can be
signed to the required values by adjusting
sponding I. Additionally, it can be seen that the PID
pa
as-
the corre-
B
rameters (Kp, K
i and Kd) can be independently con-
trolled by 12
B
B
I
I, IB3 and IB4, respectively.
3. Simulation Results
To prove rmances of the proposed the perfocontrollers,
am was used for the exami-
transistors employed in the
realize a
cl
the PSpice simulation progr
nations. The PNP and NPN
proposed circuits were simulated by using the parameters
of the PR200N and NR200N bipolar transistors of the
ALA400 transistor array from AT&T [22]. Figure 5 de-
picts schematic description of the CCCDBA used in the
simulations. These proposed circuits were biased with
corresponding input bias current IB of the CCCDBAs
with the symmetrical ±1.5 V supplies voltages.
To validate the practical application of the proposed
controllers, firstly, the proposed current-mode PID con-
trollers and passive low-pass filter were used to
osed-loop control system as depicted in Figure 6. For
the current-mode low-pass filter, the circuit is shown in
Figure 7 with an additional output terminal. The current
transfer function of the low-pass filter is found to be

1
2
12
.
1
o
lp in
ICR
HILCsRRsC    (8).
The passive elements of the filter in Figure 7
determined by R1 = R2 = 1 k, L = 1 µH and
Figure 8 shows frequency response of passive low-pass
fil
re
I = 26 µA and I= 26
µA
were
C = 1 µF.
ter employed as a plant of closed-loop control system.
Figure 9 illustrates the simulation results of the PI
controller using CCCDBAs without the plant, where C =
1 nF, input signal of 20 µA step waveform. A transient
sponse of the PI controller is shown in Figure 9(a).
Figure 9(b) demonstrates that the KPi of the PI controller
can be adjusted. The IB2 of PI controller is tuned to 13
µA, 26 µA and 52 µA where IB1 = 13 µA, IB3 = 26 µA
and C =1 nF. On the other hand, the integral conditions
variation with IB3 to 13 µA, 26 µA and 52 µA is shown in
Figure 9(c), it can be verified that the integral conditions
of the PI controller can be electronically/independently
tuned by IB3, as depicted in (5).
Figure 10 shows the simulation results of the pro-
posed PD controller without a closed-loop control system,
where C = 470 nF, IB1 = 13 µA, B2B3
, input signal of 20 µA step waveform. The simulation
result as shown in Figure 10( a) is a transient response of
the PD controller. Figure 10(b) demonstrates that the
KPD of the PD controller can be tuned. The IB2 of PD
controller is adjusted to 26 µA, 52 µA and 104 µA,
where IB1 = 26 µA, IB3 = 26 µA and C = 470 nF. On the
other hand, the derivative condition variation with IB3 to
26 µA, 52 µA and 104 µA is shown in Figure 10(c). It
B
I
1
Q
2
Q
3
Q
21
Q
4
7
Q
8
Q
9
Q
10
Q
11
Q
12
Q
13
Q
Q
5
Q
6
Q
20
Q
14
Q
15
Q16
Q17 Q
18
Q
19
Q
p
n
2
z
23
Q
CC
V
E
E
V
1
z
24
Q
1
I
1
I
25
Q
27
Q
w
Figure 5. Internal construction of CCCDBA.
26
Q
22
Q
Figure 6. A closed-loop control system.
Figure 7. The passive RLC low-pass filter used as a plant.
Figure 8. Frequency response of RLC low-pass filter plant.
can be verified that the differential conditions of the PD
3, as depicted in (8).
e elements as followed: C1 = 1
µF
novel current-mode PI, PD
controller can be electronically/independently tuned by
IB
To obtain the proposed current-mode PID controller,
whose transfer function of Kp = 1, Ti = 38.46 s and Td =
235 s, we use the passiv
, C2 = 1 nF, where IB1 = 20 µA, IB2 = 40 µA, IB3 = 50
μA and IB4 = 20 µA. We determine input signal as a step
waveform of 20 μA at 1 kHz of frequency. Figure 11(a)
shows the result of the transient response for an initial
condition obtained from the closed-loop control system
in Figure 6. Finally, Figure 11(b) shows the relationship
between input and output signals during a steady state
condition. The power consumption of the closed loop
control systems is 5.71 mW.
4. Conclusion
In this study, a synthesis of

S. SRISAKULTIEW, M. SIRIPRUCHYANUN 291
(a)
(b)
(c)
Figure 9. Simulation results of proposed PI controller.
(a)
(b)
(c)
(a)
Figure 11. Input and output relationship of PID controller
with closed-loop control system.
and PID controllers were realized by employing CCCDBAs.
All PI, PD and PID parameters can be tuned electroni-
cally and independently by the corresponding bias cur-
rents. The circuit description of the PID controller com-
prises only four CCCDBAs and two grounded capacitors.
PI and PD controller consisf three CCCDBAs coop
erating with a grounded capacitor, without any external
n control systems using a
pensation for Current Mode Step-Down Converters,” Ap.
Note SLVA350.
http://focus.ti.2.pdf
anwisut and M. Siripruchyanun,
(b)
ts o-
resistor. Simulation results confirm the theoretical analy-
sis. It is easily modified to use i
microcontroller [20]. With mentioned features, it is very
suitable to realize the proposed controllers in a mono-
lithic chip for use in battery-powered electronic devices.
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