wideband Darlington amplifier is described. The amplifier configuration consists
of a common-emitter transistor pair with low-pass filter. The normalized gain ...
Proceedings of the 1st European Wireless Technology Conference
A Novel Darlington Amplifier Optimized for Wideband Oleg V. Stukach Tomsk Polytechnic University 30 Lenin Avenue, Tomsk, 634050, Russia
[email protected] Abstract – A new design topology and performance for the ultra wideband Darlington amplifier is described. The amplifier configuration consists of a common-emitter transistor pair with low-pass filter. The normalized gain characteristic for the amplifier provides 1.36 multiple expansion of frequency band without degradation of the dynamic range, at VSWR and matching of input-output retaining. Expression for the optimum transfer factor was received. On this base the amplifier module for measuring and communication devices is created. This paper will discuss the design theory, techniques, and measurements of this newly developed Darlington circuit.
I. INTRODUCTION In the power amplifiers the Darlington transistors and the shunt voltage feedback are described of the wide applications [1–3]. Advantage of such amplifiers is increased output voltage on the small resistance load. The diagram of the Darlington amplifier with the negative voltage feedback is shown in Fig. 1. The amplifier contains transistors T1 and T2, shunt feedback on resistor R1 between the base and collector of transistor T1 and the emitter resistors R2, R3 for proper bias. Input signal is distributed between transistors, so base-emitter voltage of the transistor T1 is equal to the base-emitter voltage of transistor T2. Sharing an input voltage is produce by the choice of emitter resistors R2 and R3.
is not used completely. The use of the emitter capacity both in first and second transistors does not allow to achieve expansion of the working frequency band. Novelty of the investigation consists of optimization of the amplitude frequency characteristic for the Darlington amplifier on maximization of working frequency band using a low-pass T-filter. It is shown that frequency-dependent feedback, as well as the low-pass T-filter as delay line permits to essentially enlarge the working frequency band of amplifier in a small signal mode. II. CIRCUIT DESCRIPTION If transistor parameters are the same, the equal control voltages of transistors bring identical collector currents of T1 and T2, which summarized in common load. It is ensured an increased the output signal level in comparison with onetransistor stage. The shunt voltage feedback allows a broadband input-output matching. Besides, this feedback brings in essential improvement of the gain uniformity, as the feedback depth increased with the growing of frequency. The linear analysis of circuit was carried out by the Yparameter method. For simplification we shall consider that both transistors are identical, and it operates in the identical modes. Besides we do not account small parameters |y12|, |y22| in comparison with another one. According to Fig. 1, we receive the Y-parameter matrix as following:
0 y11 º ªy111/ R1 1/ R1 » «y 1/ R 1/ R 0 y21 21 1 1 » « Y « 0 0 1/ R3 y11 y21 y11y21 » » « 2y11 y211/ R2¼ y11 ¬y11y21 0 On the basis of the Y-matrix we shall receive expression for the transfer factor: 3 K y 21 R1 /( a 2Q ) y 21 R1 1 , y 21 /( y11 y 21 ) is the transfer factor
Fig. 1. Diagram of the Darlington amplifier
However similarly amplifiers has narrow frequency band by insufficiently contribution of transistors to output signal and insufficiently phased adding the transistors powers compare a distributed amplifier. The delayed signal on the first transistor is amplified by the second transistor. The collector current of the first transistor is less that second one, so the first transistor
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where a common base transistor, and
Q [(1 / R3 y 21 / a )( y11 1 / R2 y 21 / a ) y11 y 21 / a ]
.
(1) of the
(2)
Thereby, from (1) and (2), it is possible to conclude following.
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1. The transfer factor depends on the feedback resistance in a large degree. 2. It is necessary to reduce Q for increase of gain, but as far as y21 enters to expression (2), for ensuring of the identical contributions of both transistors in the output signal it is necessary that 1 / R2 | y 21 y11 , 1 / R3 | y 21 . Nevertheless,
Ohm, Rbb=7.25 Ohm, Rbe=565 Ohm, Cc=18.5 fF, Cbc=26 fF, Cbe=1.45 pF, W=1.3 ps, Gm0=0.38.
these conditions do not provide the maximum working frequency band because of the Y-parameters of transistors very depend on frequency in the high frequency domain. 3. It is necessary to extend the working frequency band by forcing of second transistor in relation to the input signal. The third condition is reached by following. Optimized Darlington configuration with resistive feedback (Fig. 1) with flat gain over a broad bandwidth is shown in Fig. 2. Unlike previous, the amplifier contains low-pass T-filter L1, L2, C4. The additional capacitor C4 is a forcing element for the transistor T2. It permits to increase a load voltage in accordance with frequency growing. Thus, expansion of working frequency band is reached. Fig. 3. Model of transistor
Calculated amplitude-frequency and phase-frequency characteristics of the amplifier are shown in Fig. 4 and 5 accordingly. The shaped curves (1) correspond to initial circuit without filter L1,L2,C4, continuous one – with the filter (2), optimized on the maximum frequency band. The aim function F for optimization is: F Kc K( f ) o min, where Kc is the transfer factor on average frequencies.
Fig. 2. Schematic diagram of the Darlington amplifier
Such amplifier works as follows. The input signal goes on the base of first transistor T1 and from its collector through delaying filter L1, L2, C4, goes on output. Simultaneously the input signal is repeated on emitter of the first transistor T1 and enters on the base of second transistor T2 and from its collector is transmitted to the load. Addition inductances L1, L2 and additional capacitor C4 forms the T-circuit low-pass filter for delay of channel signals. It provides an inphase summation of signals from both transistors. III. MODELING It is possible to carry out the detailed modeling of the circuit on AC with the linear physical equivalent of transistor. Model of the transistor is shown in Fig. 3, as described in [4]. Accordingly [4], the small emitter-base and base-collector capacities were not take into account. Parameters of the equivalent were chosen as following: Lb=25 pH, Lc=35 pH, Le=5.8 pH, Cep=23.3 fF, Rb=1.53 Ohm, Rc=3.2 Ohm, Re=1.1
Fig. 4. Wide band gain vs. frequency
Fig. 5. Phase vs. frequency
It is visible from Fig. 4, 5 the low-pass filter with optimum parameters increases the working frequency band in 1.36 times. For considered mathematical model a 3-dB bandwidth
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is 17.9 GHz for the initial circuit and 24.5 GHz for optimal. From Fig. 5 is seen that on frequencies, near to 21.5 GHz the phase shift of 780 is observed. This resonance promotes the bandwidth expansion. IV. EXPERIMENT Three experimental amplifiers on the different transistors were developed and amplitude-frequency characteristics were measured. All amplifiers were differed by the extended working frequency band in comparison with amplifiers on ordinary Darlington circuit [1–3]. Advantage in the frequency band makes from 1.2 up to 1.3, moreover expansion of band occurs without degradation of the dynamic range and matching conditions. It is distinctive that use the emitter capacity does not give such band expand, and the joint use of the emitter capacity and filter results the over-gain of the frequency characteristic in the upper frequencies.
[2]
[3]
[4]
Fig. 6. Photograph of the amplifier
The two-stage Darlington amplifier has 7.3 dB gain and 3dB bandwidth to 25 GHz (Fig. 6). The input and output VSWRs are less than 2.3:1 and 3.3:1. Compared to similar advanced bipolar Darlington amplifiers [2–3], these amplifiers have more gain and bandwidth more than 1.36 times compared to previously reported amplifiers. It is the highest bandwidth reported for the amplifiers with distributed gain. This design is self-biased and uses a 6 Volt supply. The total power consumed is 200 mW. The lower frequency performance of this circuit is limited by the coupling capacitor value (68 nF). V. CONCLUSION A novel Darlington amplifier has been developed which incorporates optimized low-pass T-filter. Modeling has shown that the filter parameters can change in wide ranges of elements, however new configuration results in a gainbandwidth product improvement of 1.36 times over conventional Darlington configuration. In comparison with usual amplifiers [1–3] the offered one differs by extended bandwidth. The considered circuit is used in serially produced amplifiers for measuring devices. REFERENCES [1]
D. Costa and A. Khatibzadeh, "A Wideband AlGaAs/GaAs Heterojunction Bipolar Transistor Amplifier Optimized for Low-NearCarrier-Noise Applications Up to 18 GHz", 1994 MTT-S International
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Microwave Symposium Digest 94.3 (1994 Vol. III [MWSYM]), pp. 1645-1648. K.W. Kobayashi and A.K. Oki, "A Low-Noise Baseband 5-GHz Direct-Coupled HBT Amplifier with Common-Base Active Input Match", IEEE Microwave and Guided Wave Lett., vol. 4, no. 11, pp. 373-375, November 1994. K.W. Kobayashi, D.C. Streit, D.K. Umemoto, T.R. Block, and A.K. Oki, "A Monolithic HEMT-HBT Direct-Coupled Amplifier with Active Input Matching", IEEE Microwave and Guided Wave Lett., vol. 6, no. 1, pp. 55-57, January 1996. S. Bousnina, P. Mandeville, A.B. Kouki, R. Surridge, F.M. Ghannouchi, "Direct Parameter-Extraction Method for HBT SmallSignal Model", IEEE Trans. on MTT, vol. 50, no. 2, pp. 529-536, February 2002.
