Analysis of the Impact on Amplification Due to Bypassing in an NPN Emitter -Resistor Circuit

Sandesh Mohan Adhikary and Lab Partner: Anna NuxollDepartment of Physics, Reed College, Portland, Oregon, 97202, USA

(Dated: September 16, 2013)

The impact of the bypassing capacitor in an amplifier circuit constructed using a 2N2222 NPNtransistor driven by a 10 kHz triangular waveform was analyzed by measuring gains with andwithout the capacitor connected. The measured gain of the bypassed emitter-resistor circuit of -286±13 was only 4.67 % different from the theoretical value of -300 whereas the measured gain of theunbypassed emitter resistor circuit of −15 ± 0.5 was 100 % different from the theoretical value of-7.5. The bypassing was observed to have had a significant impact on the gain, increasing it by 94.8%.

I. INTRODUCTION

The discovery of the transistor effect by John Bardeenand Walter Brattain at Bell Telephone Laboratories in1947 [1] ushered a revolution in technological progress.Paving the way forward from the clunky and time-consuming vaccum tubes, transistors enabled devices ofextreme complexity to be developed on the minute realestate on Integrated Chips. Bardeen and Brattain wereawarded the Nobel Prize in 1956 for their discovery of thetransistor effect [2].A part of almost every piece of elec-tronics present today, the transistor manages to provide arange of versatile uses even though its arsenal comprisesmainly of only two techniques - switching and amplifying[3]. The switching capabilities of transistors have allowedthem to be used in developing logic devices of immensecomplexity. However, the experiment described in thispaper focuses on the amplification of input signals withthe help of transistors.

Transistors acheive amplification by allowing a smallvoltage (or current) to control the flow of a much largercurrent[3]. The current flowing from the collector to theemitter is equal to the base current multiplied by a factorβ. The functioning of the transistor greatly depends onthe biasing regime it operates on. In a forward biasedbase-emitter regime, the requirement that needs to bemet is Vc> Vb> Ve (Fig. 1 ), where the subscripts referto collector, base and emitter. In an amplifier circuit, thebiasing requirement is met through the right combinationof biasing resistors. The DC power supply drives currentIC through RC into the collector, out the emitter andthen into the ground via Re. But even though the resistorcombination is essential in creating the amplifier circuit,the presence of the emitter resistor, Re actually counter-acts the amplification. This resistor provides a negativefeedback which, by increasing the value of Ve, minimizesVbe, the difference between Vb and Ve. Vbe representsthe voltage that the transistor acknowledges as enteringit and amplifies the output accordingly. Therefore, thepresence of Re, although important in the functioning ofthe amplifier, also reduces the amplification. In order tosolve this problem, a by passing capacitor (Cb) can beconnected in parallel to Re. The capacitor accomplishes

this because for a DC supply (the power supply for thetransistor), the capacitor is basically an open circuit withinfinite resistance. But for an AC signal, the capacitoreffectively makes the emitter an AC ground. This effectwill be analyzed in greater detail in the later sections ofthis experiment in order to obtain a quantitative mea-surement of the improvement in gain due to the presenceof this bypassing capacitor.

FIG. 1: Simple amplifier circuit. Schematic of a basic ampli-fier circuit

II. EXPERIMENTAL DESIGN

An analog bypassed emitter resistor circuit was con-structed on a breadboard as shown by the schematic di-agram in Fig 2. A voltage source (VCC) of 15 V wasused to run the 2n2222 transistor. Firstly, relevant po-tential measurements from the circuit were compared totheoretical values to check if the circuit was, in fact, op-erating in the required biasing regime and was acting asan amplifier. Secondly, the output signals (VOut) werecompared to the input signals (VIn) with and withoutthe presence of Cb in order to gauge the impact of Cb onthe operation of the circuit, with special interest in mea-suring changes in voltage gains (the amplification factor).The circuit has been designed in order to ensure forward

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biased emitter-base diode such that the voltage appliedacross the emitter-base junction needs to have the baseat a positive potential about 0.6 V greater than that ofthe emitter (i.e VBE = 0.6). Furthermore, resistors R1

and R2 are chosen to ensure I2 > IB . Lastly, the ampli-tude of the input signal should be maintained such theoutput signal does not get clipped and thus complianceis maintained.

FIG. 2: Bypassed emitter resistor circuit. This in an amplifiercircuit which amplifies Vin into Vout according to the valueof Gain as determined by the resistances. Cb acts as thebypassing capacitor.

The potentials (in relation to ground) at the base (VB),collector (VC) and the emitter (VE) are of special inter-est while analyzing the circuit. The strategy employedin theoretically obtaining these values was to analyze theDC equivalent of the circuit of interest at zeroth orderand then first order while using Kirchoff Voltage Loops(KVL) and the main computational tool. In order to ob-tain the DC equivalent of the circuit, it was firstly notedthat with DC, ω, the frequency of the input signal, iszero and thus, owing to the inverse relationship betweencapacitor impedence and input signal frequency, the by-pass capacitors essentially become open circuits and canbe removed. Furthermore, the AC voltage source in theoriginal circuit is turned into a short in the DC-equivalentcircuit. Lastly, a DC model of the transistor is adoptedwhere the transistor is replaced by a junction with a doidebiased towards the direction of the emitter and placed atthe Base-Emitter junction. These changes are shown inthe DC-equivalent circuit in Fig. 3.

A. Zeroth Order DC Circuit Analysis

By using conservation of charge, the following equa-tions are readily deduced:

FIG. 3: The equivalent DC circuit. This is the quiescentcircuit without any capacitors, the AC source turned into ashort and with the DC model of an NPN transistor used toapproximate the circuit of interest.

I2 + IB = I1 (At point j) (1a)

IC = IE − IB (At point k) (1b)

The following Kirchoff Voltage Loop (KVL) equationsdescribe the circuit presented in Fig. 3:

I2R2 +R1(I2 + IB) = VCC (2a)

IERE + VBE + (I2 + IB)R1 = VCC (2b)

IB =IE − IB

β(2c)

With the assumption that the β → ∞, IB = 0, I2 IB and IE IB , IC = IE . Now, by solving Equations 2(a-c) it is possible to obtain the following expression forIE :

IE =VCC − ( VCC

R1+R2)R1 − VBE

RE= IC (3)

Since R1 and R2 form a voltage divider circuit, it ispossible to derive the following expression for VB fromthe equations at hand:

VB = VCCR2

R1 +R2(4)

With the expression for IC in Eq. 3, the following ex-pression for VC can be derived:

VC = VCC−ICRC = VCC−VCC − ( VCC

R1+R2)R1 − VBE

RERC

(5)With these expressions, it is possible to obtain VB , VC

and VE . The results are tabulated in Table I. With theseexpressions from the zeroth order DC circuit analysis, itis possible to make the higher ordered first order analysis.

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B. First Order DC Circuit Analysis

With the assumption that β is finite (say 100), a rela-tionship between IB and IE can be established :

IB(1 + β) = IE (6)

Furthermore, from Equation (2b), it can be deducedthat:

I2R1 + IBR1 + IERE = VCC − VBE (7)

The task of finding all the required currents now in-volves solving the three simultaneous equations: 2a, 6and 7. By substituting the relevant values of R1(82KΩ),R2(10KΩ), RE(1.0KΩ), VCC(15V ) and VBE(0.6V ), thematrix equation in Equation 8 was obtained. The valueof VBE was theoretically deduced to be 0.6V since thatis the baising requirement placed on the transistor.I2IB

IE

=

92KΩ 82KΩ 082KΩ 82KΩ 1KΩ

0 101KΩ −1KΩ

× 15V

14.4V0

(8)

The resultant values of VB , VE and VC , which werefound using the values for currents and the expressionsfor the respective potentials at hand, are shown in Ta-ble I.

TABLE I: Required potentials for the zeroth and first orderresults for DC and AC analysis of the bypassed emitter resis-tor circuit

Quantity VC VB VE = VB − 0.6/, V

V V V

Zero order [DC] 7.27 1.63 1.03

First order [DC 7.97 1.55 0.95

C. Zeroth Order AC Analysis

Now, the AC zeroth order analysis is performed toobtained a higher order approximation of the emitter-resistor circuit. Maintaining the assumptions that β →∞ =⇒ ib = 0 =⇒ ic = ie, ω → ∞ =⇒ ZC = 0and that a DC source becomes a short in an equivalentAC circuit, a more complicated figure as shown in ?? isanalyzed. The AC equivalent model of a transistor con-sists of a dynamic resistance (re) between the base and

the emitter where re = ic(mA)25mV .

The following equations hold by Ohm’s Law and con-servation of charge respectively:

iere = +isr = vs (9a)

is = ib + i12 (9b)

where i12 is the current in the ground wire leading to theparallel combination of R1 and R2

FIG. 4: AC equivalent circuit. This circuit was obtained byremoving capacitors and turning DC sources into shorts alongwith applying the AC model of the transistor - the dynamicresistance re

Now, an expression for vin can be obtained:

vin = vb = vsR1||R2

R1R2 + r(10)

With vin already at hand, obtaining Vout will enablethe calculation of the gain, the quantity of compari-son between the bypassed and the non-bypassed emitter-resistor circuit. It is known that:

vout = −icRc (11)

The computation of the gain will be different for thebypassed and the unbypassed circuits. These two scenar-ios are dealt with separately below:

1. With the emitter resistor bypassed

With the bypassing capacitor present, the followingexpression can be obtained for ie:

ie = vsR1||R2

R1R2 + r(

1

re) (12)

Now, substituting the value of ie from Eq. 12 intoEq. 11, an expression can be derived for vout, which, inturn, yields the following expression for gain:

G = −VoutVin

= −Rc/ic(mA)

25mV(13)

2. With the emitter resistor not bypassed

Without the presence of the capacitor Cb, the gain canbe easily computed as:

G = − RC

RE + re(14)

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III. PROCEDURE

The experiment was conducted in three parts. Firstly,The resistances used in the circuit were separately mea-sured to ensure accurate measurements of gains. Sec-ondly, the quiescnet potentials at the three transistorterminals were measured for comparison with theoreticalvalue to ensure proper functioning of the amplifier cir-cuit. Finally, gains were measured separately with andwithout the bypassing capacitor Cb.As evidenced by equations 13 and 14, the resistancesR1, R2, RC and RE play crucial roles in determining thegain of the circuit as well ensuring that the transistor isworking within the correct biasing regime. Therefore, theexact values of these resistors were measured separatelyusing a digital multimeter and are presented in Table II.Since the circuit consists of shunt paths that force thecurrent to flow through alternate low-resistance paths,the resistances were measured separately and not whileconnected to the circuit. These values for the resistanceswill be used to obtain theoretical values of the gain forcomparison.

TABLE II: Measured and theoretical resistances for all resis-tors involved in the analog circuit being analyzed

Resistor Measured Resistance Theoretical Resistance

(kΩ) (kΩ)

±0.1kΩ

R1 81.6 82.0

R2 9.98 10.0

RC 7.39 7.5

RE 1.00 1.0

Before the circuit was driven with an external volt-age source, the quiescnet voltages at the collector (VC),emitter (VE) and the base (VB) of the bypassed emitter-resistor circuit were measured. These values were com-pared to theoretical values to ensure that the circuitwas operating in the correct biasing regime. Table IIIpresents the measured voltages along with predicted volt-ages. As the first order DC analysis provides a betterapproximation of the circuit in general than the zerothorder, the values from the former analysis, rather thanthe latter, are used as predicted voltages in Table III.

After ensuring that the circuit was operating as ex-pected, it was driven with a triangular wave at 10 kHzwith no DC offset. The input and output signals wereboth displayed on a digital oscilloscope to visually in-spect differences between the two, mainly amplitude andphase differences.At sufficiently high input amplitudes, the output voltagegets “clipped” and does not provide accurate measure-ments while computing the gain since the output voltageis not allowed to reach its natural amplitude (no compli-ance). To ensure that all observations were being madein the “unclipped” regime, the amplitude was slowly in-

TABLE III: Measurements of quiescent voltages of the collec-tor, emitter and base of the bypassed emitter-resistor circuit

Terminal Measured Voltage Average Predicted Voltage

(V )V (V ) (V )

±0.02V ±0.02V

Trial 1a Trial 2 Trial 3

Collector 15.40 8.03 8.04 8.04 7.97

Base 1.68 1.62 1.62 1.62 1.55

Emitter 1.00 1.00 1.00 1.00 0.95

aA loose connection was noticed in the circuit after measuringVC and VB . Since the only certain measurement in Trial 1 (VC) isexactly the same in all trials, the readings from Trial 1 were ignoredwhile computing the averages.

TABLE IV: VIn, VOut and Gain for the non-bypassed circuit

Vin Vout Gain

(mV ) (V )

±1V ±0.1V

50 13.9 278 ± 5.6

45 13.5 300 ± 6.7

40 13.2 330 ± 8.3

60 14.2 237 ± 3.9

creased until the top and bottom parts of the output sig-nal were seen to be conspicuosly flatting out. As shownin Figure 5, the output signal was completely unclippedat input amplitude (peak to peak) of 50mV (a). At 60mV (b), slight curving of the output signal was observedbut it still remained unclipped. As the voltage was in-creased above 60mV, the straight lines forming the train-gular wave were seen to become more curved along withthe extremes of the curve completely flattening out. Atabout 100mV (c), the signal was seen to be completelyclipped and resembeled a sinusoidal signal with flattenedextremes. In order to ensure compliance, the maximuminput amplitude applied to the circuit was 60 mV (peakto peak).Corresponding values of Vout were measured accordingto different values of Vin as shown in .Table IV for thebypassed circuit. The value of predicted gain (-300) wascomputed using Equation 13.Finally, the bypassing capacitor Cb was removed fromthe circuit and then values of Vout were measured for dif-ferent values of Vin as shown in Table V. The value ofpredicted gain (-7.5) was computed using Equation 14.

IV. DATA ANALYSIS

The values of measurements from Table III was com-pared with theoretical values to ensure that the cir-cuit was functioning predictably and was within requiredcompliance and biasing regimes. Furthermore, the mea-

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Time

Time

Time

Voltage

Voltage

Voltage

(a)

(b)

(c)

FIG. 5: Vout and Vin plots with increasing input amplitude.The top curve in each of the plots represents the output whilethe bottom represents the input. Parts (a), (b) and (c) referto input amplitudes (peak to peak) of 50 mV, 60 mV and 100mV.

TABLE V: VIn, VOut and Gain for the non-bypassed circuit

Vin Vout Gain

(mV ) (mV )

±1mV ±1mV

50 700 14 ± 0.3

40 640 16 ± 0.40

sured gains from Table IV and Table V were compared torespective theoretical values and especially with one an-other to analyze the impact of Cb on the gain of providedby the amplifier circuit.

The measured voltages as shown in Table III werefound to be consistent with the predicted values withpercentage discrepencies of 10%,0.62% and 2.9% for VC ,VB and VE respectively. Thus, the bypassed emitter-resistor amplifier circuit produced voltage measurementsas expected from an NPN amplifier circuit.As seen in all three plots in Figure 5, the output signalis definitely amplified in comparison to the input signal.The shape of the output signals also match the predic-tion that gain should be negative. As can be seen in thefigure, the output signals and the input signals have aphase difference of π i.e. the signals are reflected along

the x-axis. Therefore, even though the values of mea-sured gains have been quoted as positive, they should beunderstood to be negative to indicate the phase differ-ence between the input and output signals.The average value of gain obtained from the bypassedcircuit (286 ± 13.0) has a percentage difference of 4.7 %from the predicted value of -300. Given the errors, itseems that the predicted value lies outside the error barsof the measured values. This might be the case becausethe error due to the noise in the signal has not been incor-porated in the error estimates. On the other hand, thegain obtained from the unbypassed circuit (15± 0.5) hasa 100% difference from the predicted value of (-7.5). Thisexcessively large error is explained by the fact that thenoise to signal ratio was much higher in the case of theunbypassed output signal due to the low amplification.Furthermore, since the values being measured were peakto peak voltages, the data was especially susceptible toerrors due to noise.As is evident from comparing the value of gain from thebypassed circuit to that of the unbypassed circuit, thepresence of Cb increases the gain by about 94.8 %.

V. CONCLUSION

A simple amplifier circuit was built using a 2N222NPN transistor with the main goal of analyzing theimpact of the emitter bypassing capacitor. Furthermore,the quiescent circuit without a driving AC input signalwas also analyzed in order to understand the significanceof the combination of resistors employed in an amplifiercircuit, specifically the emitter resistor.The task of the emitter bypassing component is one thatis extremely well suited for a capacitor. Since capacitorsdo not conduct DC voltages but are able to conductAC voltages, the emitter bypassing capacitor is ableto enable the bypass the negative feedback that wouldarise due to the presence of the emitter resistor whilenot bypassing the DC current that is required for thetransistor to operate.The quiescnet circuit when analyzed without any ACinput signal, operated as predicted by theory withdiscrepencies in the values of relevant potentials rangingfrom 0.62 to 10 %. This relatively low percentage errorsexemplifies the efficiency of the emitter resistor bypass-ing capacitor. Though the function of the capacitor is tobypass AC currents form the emitter resistor, it wouldhave been a futile device if it interrupted the flow ofDC current, which is essential for the functioning of thetransistor.It was noticed that the presence of the capacitorimproves gain by about 94.8 % from about -7.5 to286. This result not only highlights the usefulness ofthe technique of bypassing the emitter but also pointsout the limitations of the transistor when operatedwithout the bypassing. If it were not for the techniqueof bypassing the emitter-resistor, the transistor may not

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have found the wide appeal as an amplifier that it enjoystoday.

VI. BIBLIOGRAPHY

[1] J. Gertner. The Idea Factory: Bell Labs and theGreat Age of American Innovation (Penguin Books,

New York, 2013)

[2] J. Bardeen. Walter Houser Brattain 1902-1987:A Biographical Memoir(National Academy of Sciences,Washington D.C., 1994)

[3] R. E. Simpson. Introductory Electronics forScientists and Engineers(Allyn and Bacon Inc., Boston,1974)