� Abstract—This contribution deals with simple and adjustable

triangular and square wave generator employing diamond transistor, two voltage controllable amplifiers, one resistor and grounded capacitor. Main aim is the exploration of adjustable features of a real circuit compared to ideal estimations. Detailed analysis and experimental tests proved that nearly ideal estimations give inaccurate results. We performed refinements corrections where existence of saturation in voltage controllable amplifier, that tunes frequency, was considered in calculations. Results proved possible controllability in discussed solution but reveal also high dependence of features (repeating frequency and produced amplitudes) on features of particular active element (mainly voltage controllable amplifier) in the design because each active element has little bit different output saturation levels (dependent on fabrication tolerance, etc.).

Keywords—Diamond transistor, electronic control, gain adjusting, voltage controllable amplifier, triangle and square wave generator.

I. INTRODUCTION odern controllable active elements [1] allow design of interesting applications consisting of minimal number of active and mainly passive parts (resistors,

capacitors). Typical example is a functional (triangular and sine wave) generator. In the past, at least three resistors and one floating capacitor were necessary for construction of functional generator employing operational amplifiers. However, lack of direct electronic controllability in circuits with operational amplifiers is evident. A controllable replacement of a floating resistor is suitable for tuning of repeating frequency. Very good examples of such solution were discussed in [2]. Diamond transistor and voltage controlled amplifiers [3]-[7], which are in this paper used to realize a Schmitt trigger [8], are very popular active elements

Manuscript received February 21, 2013. Research described in the paper was supported by Czech Science Foundation projects under No. 102/09/1681 and by internal grant No. FEKT-S-11-13. The support of the project CZ.1.07/2.3.00/20.0007 WICOMT, financed from the operational program Education for competitiveness, is gratefully acknowledged. The described research was performed in laboratories supported by the SIX project; the registration number CZ.1.05/2.1.00/03.0072, the operational program Research and Development for Innovation.

R. Sotner (corresponding author) and J. Petrzela are with the Dept. of Radio Electronics, Brno University of Technology, Brno, Technicka 12, 616 00 Czech Republic. (e-mail: {sotner, petrzelj}@feec.vutbr.cz).

J. Jerabek, N. Herencsar and K. Vrba are with the Dept. of Telecommunications, Brno University of Technology, Brno, Technicka 12, 61600 Czech Republic (e-mails: {jerabekj, herencsn, vrbak}@feec.vutbr.cz). A. Lahiri, 36-B, J and K Pocket, Dilshad Garden, Delhi, India (e-mail: lahiriabhirup@yahoo.com)

in many various applications. Interesting suggestions were given in [3] where diamond transistor (DT) is the main core of presented behavioral models of advanced active elements. In the most cases, diamond transistors allow design of applications with minimum number of passive elements and grounded capacitors. Several simple solutions of generators utilizing modern active elements, with respect to classical operational amplifier-based concepts, already exist. Brief discussion is provided in following text. Biolek et al. [9] employs simple solution utilizing single current differencing transconductance amplifier (CDTA) and three resistors with grounded capacitor. Two current conveyors of second generation (CCIIs) and six resistors with floating capacitor were used by De Marcellis et al. [10]. Chien et al. [11] utilized two differential voltage current conveyors (DVCCs), three resistors and grounded capacitor. Two CCIIs, three resistors and two grounded capacitors required generator presented by Almashary et al. [12]. The same number of CCIIs, three resistors and floating capacitor used Pal et al. in [13]. Two popular current feedback amplifiers (CFOAs) were utilized also by Saque et al. [14] together with four resistors and floating capacitor. Lo et al. [15] focused his work on implementation of operational transresistance amplifiers (OTRAs) and presented solution requires three resistors and floating capacitor. Minaei et al. [16] combined construction with CFOAs and DVCCs. All discussed works supposes tuning of f0 by variation of resistor value only. However some electronically adjustable conceptions were also introduced. First of all, transconductors (OTAs) seems to be very useful in functional generators as was shown by Chung et al. [17] where three OTAs, two grounded resistors and capacitor were implemented. Transconductance of the OTA is simply controllable by DC bias current [1]. Similar solution introduced Siripruchyanun et al. [18]. Approach presented by Kumbun et al. [19] should be also noted. Their solution is based on two so-called multiple-output through transconductance amplifiers (MO-CTTAs) controlled by the DC bias current and using a grounded capacitor only. Interesting and simple circuits were proposed by Silapan et al. [20] and Sristakul et al. [21]. They employ only two multiple-output current controlled current differencing amplifiers (MO-CCCDTAs) and grounded capacitor in generator. However, all solutions presented in [19]-[21] provide current outputs only. Therefore additional current to voltage conversion is necessary. Main performances of discussed solutions and the proposed circuit are compared and summarized in Table I.

Practical Aspects of Operation of Simple Triangular and Square Wave Generator Employing Diamond

Transistor and Controllable Amplifiers Roman Sotner, Jan Jerabek, Norbert Herencsar, Abhirup Lahiri, Jiri Petrzela, and Kamil Vrba

M

431978-1-4799-0404-4/13/$31.00 ©2013 IEEE TSP 2013

TABLE I COMPARISON OF PROPOSED AND DISCUSSED SOLUTIONS

Ref

eren

ce

No.

of p

assi

ve e

lem

ents

No.

of a

ctiv

e el

emen

ts

Floa

ting

capa

cito

r

Type

of c

ontro

l (P

E- p

assi

ve e

lem

ents

; D

C V

- D

C b

ias

volta

ge;

DC

I - D

C b

ias c

urre

nt)

Dut

y cy

cle

cont

rol

avai

labl

e (N

/A -

not

avai

labl

e)

Type

of o

utpu

t sig

nals

(c

urre

nt o

r vol

tage

)

Low

-impe

danc

e vo

ltage

out

puts

av

aila

ble

(vol

tage

-m

ode

oper

atio

n)

[9] 4 1 No PE N/A voltages No [10] 7 2 Yes PE N/A voltages No [11] 4 2 No PE / DC V Yes voltages No [12] 5 2 No PE N/A voltages No [13] 5(6) 2 Yes PE N/A voltages No [14] 5 2 Yes PE N/A voltages Yes [15] 4 2 Yes PE N/A voltages N/A [16] 4 2 No PE N/A voltages Yes [17] 3 3 No DC I Yes voltages No [18] 3 3 No DC I Yes voltages No [19] 1 2 No DC I N/A currents No [20] 1 2 No DC I N/A currents No [21] 1 2 No DC I N/A currents No [26] 4 2 No DC V N/A voltages No our 2 3 No DC V Yes voltages Yes

We proposed quite simple solution of a triangular and square wave generator employing one diamond transistor, voltage control of repeating frequency (f0) by voltage controllable amplifier (VCA) [6]-[7], Schmitt comparator [8] employing VCA and only one resistor and grounded capacitor. Despite of simplicity, some practical aspects, which are not so clear at the first sight, can be found and influence expected behavior of application. Almost ideal behavior of the generator is derived and discussed. More accurate description takes into account limited DC transfer characteristic and output voltage limitation. Experiments prove expected behavior which highly depends on real features of active elements in simple circuits. Main advantages of our solution are: simplicity, low number of passive elements and simple electronic control by DC voltages. High dependency of features of the application on specific parameters of active elements and necessity of three active elements were found as the most important disadvantages.

II. PROPOSED GENERATOR Generator shown in Fig. 1 utilizes two controllable voltage

amplifiers (adjustable gain A) and diamond transistor [3]-[5] including also voltage buffer (low-impedance outputs are available). Simple circuit in Fig. 1 combines comparator with hysteresis (so called Schmitt trigger [8], [17]) based on VCA2 and integration part. This part consists of voltage controllable amplifier VCA1, diamond transistor, resistor and grounded capacitor. Gain of the VCAs is given by very simple form A = 10-2(VSETA+1) [6]-[7].

A. Discussion of ideal behavior We suppose high linearity and sufficiently large dynamical range of VCA1 and DT (larger than maximum peak-to-peak value of processed signal level) in our first attempt. A sufficient dynamic range of VCA1 in integration part (VCA1, R, DT, C) is critical. Expected theoretical voltage level resolution of generated waveforms in time domain is indicated in Fig. 2. We take into account different levels of input (reference) and output voltage of the comparator due to

Fig. 1. Proposed generator using DT and VCAs.

Fig. 2. Segment of output waveforms.

-2.0

-1.0

0.0

1.0

2.0

-2.0 -1.0 0.0 1.0 2.0

V out [V]

V inp [V]

VCC = ± 5 V; ramp excitation, 10 Hz

A2

= 2.

0 (V

SETA

2 = -

1.15

V)

A2

= 5.

8 (V

SETA

2 = -

1.38

V)

A2 =

100

(VSE

TA2 =

- 2.

0 V)

Fig. 3. Measured DC characteristic of Schmitt comparator based on VCA2. low and finite gain of amplifier (triangle signal has lower peak-to-peak amplitude).

The output square wave signal VSQ achieves values given by positive and negative saturation levels (desired) of comparator with VCA2 (VSQ = ±Vsat_VCA2), see Fig. 3. Input reference thresholds (causing turn over of output signal from positive to negative saturation respectively) increases with higher gain, A2 should be > 5 for sufficient operation.

The triangular wave signal is given by voltage across capacitor (VTR = ±VC) which achieves two reference thresholds (necessary to have A2 > 1):

� �2_2

22_

1VCAsatVCAinpC V

AA

VV ����

�

� �� � , (1)

� �2_2

22_

1VCAsatVCAinpC V

AAVV ��

�

�

� ����� , (2)

and relation between ranges of voltage alternation (�VC as ±VC and �Vsat_VCA2 as ±Vsat_VCA2) is given by:

432

CVCAsat VA

AV ����

�

��

��12

22_

, (3)

where 2_2_2_2_ 2)( VCAsatVCAsatVCAsatVCAsat VVVV ��� �� , (4)

2_2_2_ 2)( VCAinpVCAinpVCAinpC VVVV ��� �� . (5) Accurate calculations require knowledge of DC transfer

characteristic shown in Fig. 3 because term A/(A�1) is valid in ideal case only and is subject to significant deviation. Charging and discharging of the capacitor to reference thresholds +VC (+Vinp_VCA1) or –VC (-Vinp_VCA1) during one period (Fig. 2) of the generated wave we can express as:

1max_

2

22_

12 T

CI

AAV C

VCAsat ����

�

� � , (6)

2max_

2

22_

12 T

CI

AAV C

VCAsat �����

�

� � . (7)

The current IC_max is supplied from Vsat_VCA2 through the inverting gain -A1 of VCA1 in case of linearity and sufficient dynamical range of VCA1. The output voltage of VCA1 is transferred to current by the resistor R and mirrored to the capacitor by the diamond transistor. The diamond transistor realizes also auxiliary voltage to current conversion of the DC component Vd to the overall output current ±IC_max. We can express discussed behavior by equations:

RVAV

I dVCAsatC

� 12_

max_, (8)

RVAV

I dVCAsatC

��� 12_

max_. (9)

The substitution of (8)-(9) to (6)-(7) provides:

112_

2

22_

12 T

RCVAV

AAV dVCAsat

VCAsat

���

�

�

� � , (10)

212_

2

22_

12 T

RCVAV

AAV dVCAsat

VCAsat

����

�

�

� � . (11)

Charging and discharging time intervals imply from (10)-(11) as:

���

�

� �

�2

2

12_

2_1

12A

AVAV

RCVT

dVCAsat

VCAsat , (12)

���

�

� ��

�2

2

12_

2_2

12A

AVAV

RCVT

dVCAsat

VCAsat , (13)

and the complete repeating frequency (T = T1 + T2) as:

���

�

� �

���

�

���

��

�

�

��

2

2

12_12_1

0 14

111

AARC

AVV

AVV

A

Tf VCAsat

d

VCAsat

d

. (14)

The voltage Vd is adjustable parameter suitable for control of the duty cycle (D) defined as:

� �nAV

VTT

DVCAsat

d �����

�

���� 1

211

21

12_

1 , (15)

where n is parameter that represents relation between the duty cycle and the repeating frequency because Vd = n.Vsat_VCA2.A1. In fact, Vd (converted to current by R) represents the DC

component of the triangular response causing adjustable shift of the signal in direction of vertical axis. Maximal and minimal D (0% or 100%) is theoretically limited to ±Vsat_VCA2.A1. The repeating frequency can be tuned independently on D by A1 in case of fulfilled condition of the constant ratio n = Vd/(Vsat_VCA2.A1). The repeating frequency simplifies in case of D = 50% (Vd = 0 V) to following form:

���

�

��

��14

1

2

210 A

ARCA

Tf . (16)

B. Restricted dynamical range of VCA1

The second discussed way takes into account limited dynamical range of VCA1 (Fig. 4). This fact specifies situation because current IC_max is supplied (converted) from the saturation voltage Vsat_VCA1 instead of VOA1 = �A1.Vsat_VCA2 gained only through -A1 of VCA1. Therefore, inequality of VOA1 � (±Vsat_VCA2)A1 for Vsat_VCA2 > max(Vinp_VCA1) influences accuracy of eqs. (10)-(15) and different equations for the design evaluation of the repeating frequency and the duty cycle are valid. The basic boundary between both “regimes of operation” is given by the maximal available linear range of VCA1 (the most critical), i.e. max(Vinp_VCA1) dependent on A1. Charging and discharging periods are given by:

dVCAsat

VCAsat

VV

RCA

AVT

���

�

� �

�1_

2

22_

1

12, (17)

dVCAsat

VCAsat

VV

RCA

AVT

�

���

�

� �

�1_

2

22_

2

12, (18)

where Vsat_VCA1 is the saturation voltage in case of lower dynamical range of VCA1 than voltage available from output of VCA2 (Vsat_VCA2). The repeating frequency and the duty cycle have form:

���

�

��

���

�

���

��

�

�

�14

11

2

2

2_

1_1_1_

0 AA

RCVV

VV

VV

fVCAsat

VCAsat

d

VCAsat

dVCAsat

, (19)

� �nV

VDVCAsat

d �����

�

��� 1

211

21

1_

, (20)

where n = Vd/Vsat_VCA1 is different than in previous case. In fact, VOA1 (Vsat_VCA1) can be measured and Vsat_VCA2 is available as VSQ. Therefore, all parameters are accessible during the measurement.

C. Additional parasitic influences Real value of the resistor (R) connected to emitter of DT should be increased when value of the intrinsic resistance (RE) is considered. The stray nodal capacitance (CP, in parallel to working C) causes high spread and inaccuracy of the repeating frequency if small values of the working capacitor (tens, hundreds of pF) are used. In case of 50% duty cycle (Vd = 0), the approximate equation for the repeating frequency is:

� �� � ���

�

��

�14 2

2

2_

1_0 A

AVCCRR

Vf

VCAsatpE

VCAsat . (21)

433

-2.0

-1.0

0.0

1.0

2.0

-2.0 -1.0 0.0 1.0 2.0

V out [V]

V inp [V]

VCC = ± 5 Vramp excitation, 10 Hz

A 1 = 0.60 (V SETA1 = - 0.89 V)

A 1 = 0.28 (V SETA1 = - 0.72 V)

A 1 = 1.66 (V SETA1 = - 1.11 V)

A 1 = 4.37 (V SETA1 = - 1.32 V)

V OA1 = V sat_VCA1= f (A 1, V sat_VCA2)[V sat_VCA2 > max (V inp_VCA1)]

V OA1 = A 1.V sat_VCA2

[V sat_VCA2 < max (V inp_VCA1)]

Fig. 4. An example of measured DC characteristics of VCA1.

III. EXPERIMENTAL VERIFICATION AND REAL BEHAVIOR We established discussed circuit (Fig. 1) on solderless

board and provided several tests. Many drawbacks are connected to using of solderless breadboard (high parasitic capacitances and parasitic feedbacks - it was not taken into account). Nevertheless, solderless breadboard is sufficient for prompt and preliminary experimental tests. Further detailed analyses will come later. However, experiments confirmed possible validity of main explanations.

We used popular diamond transistor [4] and voltage controllable amplifiers [6]. They are classified as obsolete but new replacements with improved features exist [5], [7]. However, DIP packages of mentioned elements are suitable for preliminary experiments with solderless breadboard. Behavior of the real circuit is highly dependent on features of used VCA as comparator and their saturation output voltages. Passive elements were selected as follows: R = 1 k�, C = 100 pF. Supply voltage was ± 5 V. We obtained peak-to-peak voltage levels in important nodes for specific settings. The voltage Vsat_VCA1 was 1.0 V (A1 = 1.29; VSETA1 = -1.05 V) and square wave output (Vsat_VCA2) reached 1.66 V (A2 = 5.8; VSETA2 = -1.38 V). Three sources of parasitic capacitance are important: input impedance of VCA2 (� 1 pF) [6], output capacitance of collector - current output of DT (� 5 pF) [4] and input of voltage buffer in frame of DT (2 pF). Overall value of Cp is 8 pF. Intrinsic resistance of the emitter of DT has value RE = 13 � [4]. Considering above discussed parameters eq. (21) modifies to:

� �� � 66.110.813421.1

121_

0 �

�� �CR

Vf VCAsat . (22)

Estimated value of f0 for D = 50% in accordance to (22) is 1.66 MHz. Measured value was 1.49 MHz. Achieved transient responses are in Fig. 5. Adjustability of f0 was verified experimentally in range from 0.5 MHz to 2.01 MHz by adjusting of A1 (VSETA1) and Vsat_VCA1 from 0.31 to 1.5 V (A1 between 0.29 and 2.56, VSETA1 from -0.73 to -1.20 V). Expected values calculated from (16), where parasitic influences (RE, Cp) were considered, and (21) or (22) respectively are compared in Fig. 6. It is expected that with higher values of A1 the linear range for the VCA1 reduces and there is more gain saturation of VCA1 leading to a reduced average gain and to drop in frequency. This is clear from Fig. 6 wherein at higher values of A1 there is a larger

Fig. 5. Measured transient responses of generator for D = 50%, Vsat_VCA1 = 1.0 V (A1 = 1.29, VSETA1 = -1.05 V).

0

1

2

3

0 1 2 3 4

A 1 [-]

f 0

[MHz]

VCC = ± 5 V

A 2 = 5.8

VSETA2 = -1.38 V

0.2

9

0.42 0

.67

1.2

9

2.5

6

V OA1 [V]

measured

calculated - eq. (16) V sat_VCA2 < max (V inp_VCA1)

calculated - eq. (21) V sat_VCA2 > max (V inp_VCA1)

Fig. 6. Measured and calculated dependences of repeating frequency on VOA1 (output voltage of VCA1) and voltage gain A1.

Fig. 7. Measured transient responses for D = 25%. difference in frequency from the expected value. The generator allows setting of the duty cycle. Test of this feature was provided and results are in Fig. 7. Parameters were set experimentally as: Vd = 0.4 V, Vsat_VCA1 = 0.98 V (A1 = 1.2, VSETA1 = -1.04 V), D = 25 % and f0 = 1.05 MHz.

IV. CONCLUSION Simple triangular and square wave generator based on diamond transistor, two voltage controllable amplifiers, one resistor and capacitor was studied in this contribution. Optimistic and idealized way supposes sufficient dynamical range of amplifier which serves for control of repeating frequency. However, determined principles and equations are quite far from reality. DC transfer characteristics have major impact on features and their accuracy (repeating frequency, etc.). Important problem is restricted DC transfer

434

characteristic of VCA1 because current which is charging or discharging of the capacitor is not derived from Vsat_VCA2 but, unfortunately, from saturation voltage of VCA1. Detailed study of real behavior allowed to reveal and explore main impacts that lead to specified corrections of determined design equations. However, parameters of active elements (DC characteristics) indicate main features of generator in similar solutions consist of a minimal number of passive elements and it is, in fact, also one of the important conclusions of the work. Our conclusions were confirmed by experiments with available ICs. The current gain control can be easily applied with advantages of the wider DC input range [22]-[24]. Using of low gains (current gain for example) and active elements (realizes tuning) with larger DC transfer characteristics than output levels of the used Schmitt comparator can be considered as a method how to eliminate problem. Low gain allows less narrow range of input voltages. Therefore, adjusting of the low gains (tenths and units) should ensure the operation near to ideal description. It is topic for our future work. The idea of the voltage and digital way of control in generators is actual and interesting topic. Both methods allow simple driving from peripheral blocks (D/A converter) or directly from I/O ports of microprocessors. Interesting contributions to recent progress in this field were discussed also in [25]-[26].

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[19] J. Kumbun, M. Siripruchyanun, “MO-CTTA-based electronically controlled current-mode square/triangular wave generator,” in Proc. of the 1st International Conf. on Technical Education (ICTE2009), Bangkok, 2010, pp. 158–162.

[20] P. Silapan, M. Siripruchyanun, “Fully and electronically controllable curren-mode Schmitt triggers employing only single MO-CCCDTA and their applications,” Analog Integrated Circuits and Signal Processing, vol. 68, no. 11, pp. 111-128, 2011.

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[26] M. Janecek, D. Kubanek, K. Vrba, “Voltage-Controlled Square/Triangular Wave Generator with Current Conveyors and Switching Diodes,” International Journal of Advances in Telecommunications Electrotechnics, Signals and Systems, vol. 1, no. 2-3, pp. 1–4, 2012.

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