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Learning electronic circuits using Multisim: A case study – the Darlington Amplifier

L.C. Molina Torres(molina@lme.usp.br), D. Consonni (dconsoni@lme.usp.br) Dept. of Electronic System Engineering Escola Politécnica, University of São Paulo Brazil


The objective of this note is to illustrate to second year Electrical Engineering students the importance of using a simulation software, such as Multisim [1], in order to learn faster and to better understand the procedures involved with the design and analysis of electronic circuits. As a case study, we present the Darlington Amplifier [2], introducing bipolar junction transistor (BJT) as current amplifiers and employing well-known models to explain their operation. The analysis starts by obtaining the circuit operating bias point, from a circuit schematics composed with Multisim library components, including BJT non-linear models. The transfer curve (voltage output versus input current) is traced, by DC sweeping the input current source around the quiescent point. On this characteristic curve, the student can easily visualize the potential linear and non-linear regions of circuit amplification. Using the BJT model parameters determined at bias point, linear DC models are built to replace the transistors in circuit schematics, and the transfer curve is again obtained. Its unreal linear shape is superimposed and compared to the former characteristic. An AC analysis is then performed, using the original Multisim BJT models: magnitude and phase AC amplifier responses are calculated, as the input signal frequency is varied.

Again from the bias point results, π-hybrid BJT model [2] parameters are extracted and the AC analysis is repeated inserting these models into the amplifier schematics. AC frequency performance is then compared to the previous responses. The Transient analysis is very useful to demonstrate the effects produced by device non-linearity and input signal level and frequency on the amplifier output voltage. Finally, the Fourier and Distortion analysis produce useful practical results for amplifier design purposes.

Table of Contents

1. Darlington amplifier schematics 2. Bias operating point and DC transfer characteristic 3. BJT DC linear modeling 4. Amplifier AC frequency response

5. BJT pi-hybrid model 6. Amplifier transient analysis 7. Amplifier Fourier and Distortion analysis 8. Comparing analysis methods and transistor models 9. Conclusions 10. References

1. Darlington amplifier schematics

Figure 1 shows the amplifier circuit as seen in the Multisim schematic capture stage, where BJTs Q1 and Q2 are arranged in a Darlington configuration which produces amplification of the input current signal represented by IENT, extracted at the circuit output voltage, named VS. PN2222 and PN2907A are components of the Multisim Master Database, Transistors Group, BJT_NPN and BJT_PNP Families respectively. Circuit biasing is provided by the 6V DC V1 voltage source.

Figure 1. Darlington Amplifier Circuit

The Darlington amplifier is used to introduce the bipolar transistor as an amplification element to our Electrical Engineering students. It features some interesting characteristics such as a high input impedance and unit voltage gain, which are convenient for understanding small-signal amplifier response. As a consequence of the high input impedance of the Darlington module, practically all input current signal feeds the parallel association of the two biasing resistors R4 and R5 (resulting in this case an equivalent resistance of 33kΩ), generating the input voltage to Q1, which is transferred to the output VS with unit gain. Therefore the amplifier transresistance (ratio between output voltage variation and input current variation) approximates the circuit equivalent input resistance, which is 33kΩ in the schematics shown in Figure1.

2. Bias operating point and DC transfer characteristic

Determination of the transistors’ operating point (also named quiescent point or bias point) is the first thing to do when one is analyzing an amplifier circuit. Multisim performs this simulation in the DC Operating Point analysis, using a nonlinear Ebers- Moll based model [3]. In this type of analysis, the program assumptions are that all AC sources are null, capacitors are replaced by zero-current elements (open circuit) and inductors are substituted by zero-voltage elements (short circuit). The results of this simulation are all the DC node voltages, the collector and base currents, the base-emitter voltages, the collector-base voltages and the small-signal parameters for the BJT at the corresponding bias point set by the DC sources. Variables of the circuit and device/model parameters of interest can be chosen in the DC Operating Point analysis window at the Output Tab. Table 1 shows the results of DC operating point, (calculated for IENT = 0 ) produced by the 6V voltage source in circuit of Figure 1.

Table 1. Results of DC Operating Point Analysis

On the left side of Table 1, V(1), V(2), V(3), V(4) and V(vs) are node voltages,

I(q1[ic]) and I(q2[ic]) are the collector currents IC, I(q1[ib]) and I(q2[ib]) are the base currents IB, @qq1[vbe] and @qq2[vbe] are the base-emitter voltages VBE and finally

@qq1[vbc] and @qq2[vbc] are the base-collector voltages VBC ( all DC values) for Q1 and Q2 respectively. On the right side of the same Table are the small-signal parameters of the bipolar transistors. Results from Table 1 used on Postprocessor Window enable entering expressions such as, IC/IB and gm/gpi, in order to calculate respectively DC and AC transistor current gains at the quiescent point, as shown in Table 2. These parameters will be used in the next steps of circuit analysis.

Table 2DC and AC transistor current gains

The DC analysis follows with a DC Sweep analysis, in order to obtain the DC amplifier transfer characteristic V(VS) x IENT. On this curve, base-emitter and collector-base voltage variations with IENT for both Q1 and Q2 transistors are also superimposed. The results are shown in Figure 2.

Figure 2. Results of the DC Sweep Analysis

It is interesting to notice in Figure 2, the distribution of BJTs operation region as a function of the IENT current source level:

Q1 is in the cut-off region for IENT lower than approximately – 70µA Q2 is in the cut-off region for IENT lower than approximately – 45µA Q1 is in the saturation region for IENT higher than approximately 110µA Q2 is in the saturation region for IENT higher than approximately 35µA

This means that the bipolar transistors are simultaneously in the active region for IENT varying between – 45µA and 35µA approximately. It can be seen that the strictly linear region of the amplifier DC transfer characteristic (Figure 3) is limited by these values, but the curve can still be considered fairly linear within the broader limits from -70µA and 110µA. The slope of this characteristic in its linear region results in a value equals to 33kΩ, corresponding to the DC transresistance.


Q1and Q2 Active Region




Figure 3. Amplifier DC Transfer Characteristic

3. BJT DC linear modeling

For a limited range of currents and voltages around the bias point, the highly non-linear operation of BJT devices can be simulated with a linear model as shown in Figure 4.

Values of the parameters Rx, VBE and Ro can be taken from Table 1, lines 1 and 8 at the right side, ( making Rx = 1/gx ), lines 8 and 12 at the left side (VBE) , and lines 4 and 1 at the right side ( making Ro = 1/go) for Q1 and Q2 respectively. BetaDC values can be extracted from Table 2.

Figura 4. BJT DC Linear Model

When the bipolar transistors are replaced by the DC linear model of Figure 4, the new schematics of the Darlington Amplifier will result in the circuit shown in Figure 5.

Values of VBE in Multisim are positive for both Q1 and Q2, so VBE voltage generator must be placed with the correct polarity in the circuit, in order to represent NPN and

PNP structures, respectively. The controlled current generators inject current from collector to emitter for the NPN BJT and from emitter to collector for the PNP BJT.

Q1 and Q2 in the active region

Figure 5. Darlington Amplifier Circuit with BJT DC linear models

The results obtained from the DC Sweep analysis of circuit schematics shown in Figure 5, are displayed as a blue trace in Figure 6. For comparison, the red trace refers to the same simulation using non-linear models. As can be seen, a good fit is observed in the region close to the bias point, indicating that the amplifier presents a linear performance while both transistors are operating in the active region. The use of the linear models helps in getting a better visualization of the amplifier linear operation region. However, by comparing both curves, the students should realize the limitations of this simplified linear model and its inability for predicting full-range amplifier performance.

Figure 6. DC Sweep Analysis results for both linear and non-linear models

V(VS) - Multisim Non-linear Model

V(VS) - Linear Model

Bias Point

4. Amplifier frequency response

The next step is to perform an AC analysis in order to investigate the amplifier operation with frequency variation of a sinusoidal input signal. In this simulation, Multisim uses a


BJT AC linear model (pi-hybrid model) with the parameters calculated at the bias point. The results obtained are the gain magnitude and phase curves as functions of frequency. The circuit schematics used for this analysis is shown in Figure 7. In Figure 8, the magnitude and phase frequency responses of the amplifier output voltage VS are Figure 7. Schematics for AC Analysis

Figure 8 - Amplifier frequency response (VS) as resulted from AC analysis

The amplifier low-frequency transresistance can be obtained from (Vs) low-frequency magnitude (Vmax indicated by cursor 1 (x1, y1) in Figure 8), resulting: Vmax / IENT = estimated in sections 1 and 2 above.

The cut-off frequency can be determined by locating the point where V(Vs) magnitude drops to Vmax/√2 (indicated by cursor 2 (x2, y2) in Figure 8), resulting in a value of 1.08MHz approximately.

The values of the amplifier transresistance (magnitude and phase) were calculated for other frequencies as listed in Table 2.

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