Abstract—The design and analysis of the multistage common emitter (CE) amplifier for improved voltage gain over the single stage CE amplifier is presented in this paper. The design procedure started with the design of a single stage CE amplifier. The design specifications for the CE amplifier were specified. The design of the multistage CE amplifier was done using the designed single stage CE amplifier as the basic configuration. The designed single stage and multistage CE amplifiers were simulated in the linear technology simulation program with integrated circuit emphasis (LT SPICE). The results obtained show that using analytical method a voltage gain of 45 dB was obtained for the single stage and 54 dB was obtained for the multistage respectively, the LT SPICE simulation software presented a result of 44 dB for the single stage and 54 dB for the multistage. The proposed amplifier may find suitable applications in devices operating in the low frequency such as audio signal applications. Furthermore, judging from these results coupling of more stages of the transistor amplifier to obtain greater voltage, current and power gains is recommended.
Index Terms—Amplifier, Common Emitter Transistor, Hybrid Parameter, Low Frequency Applications, Voltage Gain.
I. INTRODUCTION
With the advancement in the field of electronics, bipolar junction transistors (BJTs) have gained huge popularity, but it was not the first three terminal devices that were invented.
Before transistors came into existence vacuum tubes were used. But the major problem was, as the complication of the circuits increased more and more triodes were required to be integrated which led to more space consumption. The power consumption and current leakages which accounts for less reliability was also a challenge, so instead of controlling electrons in vacuum scientist began to think of ways to control it in solid materials, and found out that by making two point contacts very close to one another, they could actually make a three terminal device. Thus the first point contact transistor was made by using germanium, paper clip and razor blades [1].
Shockley developed the BJT by pressing together thin slices of different semiconductor materials. The transistors replaced the vacuum tubes and made a dramatic change in the world of electronics. After which integrated circuits
Published on October 20, 2019.
D. E. Dan-Abia is with the Electrical/Electronic and Computer Engineering, University of Uyo, Nigeria (e-mail: [email protected]).
A. B.Obot is with the Department of Electrical/Electronic and Computer Engineering, University of Uyo, P.M.B 1018 Uyo, Nigeria. (e-mail:
K. M. Udofia is with the Department of Electrical/Electronic and Computer Engineering, University of Uyo, P.M.B 1018 Uyo, Nigeria. (e- mail: [email protected]).
(ICs) came into existence which placed all components on one single chip [2] Bipolar junction transistor encountered problems such as surfaces getting easily contaminated and unstable surface effect, this was solved when William Shockley went ahead to invent the positive-negative (p-n) junction transistor [3]. A transistor is a semiconductor device that can both conduct and insulates. A transistor can act as a switch and as an amplifier. It converts audio waves into electronic waves and a resistor, controlling electronic current [4]. Transistors have very long life, it is smaller in size, can operate on lower voltage supplies. Basically, there are of two types, the BJT and the field effect transistor (FET) [5],[6],[7].
It is also important to mention that although BJT’s are of great importance, there are some challenges associated with them in that BJTs are current operated devices rather than voltage operated. This implies that majority of the time there is higher power consumption [8]. Also, BJTs have an input- output relationship that can be basically inverted by biasing the terminals opposite to their intended design. This means that a sloppy amplifier design can easily end up with positive feedback, and therefore becomes unstable.
Furthermore, BJTs have lower input impedance. This means a higher output impedance device may not couple very well to the input of a BJT amplifier [9].
II. REVIEW OF RELATED WORKS
The common emitter (CE) amplifier design has been proposed by several authors as a way of obtaining reasonable amplifier performance parameters, The authors in [10] proposed a similar configuration to the one proposed in this paper, but the circuit considered was a single stage and the simulation tool used was a personal simulation program with integrated circuit emphasis (PSPICE), and a voltage gain of 43 dB was obtained [11], using windows simulation program with integrated circuit emphasis (WINSPICE) for simulation of a multistage CE amplifier circuit and obtained an overall gain of 98 dB. According to [12], the analyses of frequency compensation techniques for single and multistage amplifiers were presented using the Hewlett simulation program with integrated circuit emphasis (HSPICE) for the simulation. However, [13] introduced frequency and phase response of single and multistage CE amplifier to investigate effects of cascading but output waveforms or distortion rates were not indicated, only codes were displayed.
Design and Analysis of a Multistage Common Emitter Amplifier for Low Frequency Applications
Dan Dan-Abia, Akaninyene Obot, and Kufre Udofia
III. METHODOLOGY
The most important parameter for the design of a CE amplifier is obtaining a direct current (DC) beta (β) of suitable value from the data sheet of a 2N2222 transistor. β varies in the range of 50 to 300. The value of β varies depending on the BJT fabrication techniques and process tolerances [14].
A. Design Method for the Single Stage CE Amplifier To design the single stage CE amplifier, certain parameters and specifications such as choice of transistor and direct current (DC) bias points must be considered.
The single stage CE amplifier with the circuit configuration is designed to meet the specification shown in Table I, it is assumed that β is 100 and the use of n-p-n transistors were used.
TABLEI:TRANSISTOR PARAMETERS AND SPECIFICATION
Parameters Specifications
DC supply voltage (Vcc) 15 V
Base Emitter voltage (VBE) 0.7 V Input supply voltage Vin (t) 10mVsin(2πft)
Frequency (f) 10 kHz
Quiescent Emitter collector
current(ICQ) 2.85 mA
Emitter collector voltage (VCE) 8-10 V
The DC equivalent circuit of the amplifier stage is obtained by opening all capacitors and shorting all input sources. Biasing resistances are designed to make the transistor operate in the active region. Fig. 1 shows the DC equivalent for the single stage CE amplifier.
Fig. 1: DC equivalent circuit for a single stage CE amplifier
According to [6] the analysis of a common emitter amplifier begins with designing for a specified quiescent operating point with a specified stability, the stated specifications in Table I establish three constraints among the four resistors and in the circuit therefore, one of the resistors can be obtained by using the VCC specification in Table I to satisfy some other conditions. Thus, the emitter resistor (RE) is chosen in this case so that the voltage drop across it is 1.5 V (10 percent of VCC) when IC=2.85 mA Thus, the design equations are given in (1) to (8).
𝑅𝐸=𝑉𝑅𝐸
𝑉𝐶𝑄 (1) Where VRE is the voltage across RE, IC=ICQ Quiescent collector current.
Substituting VRE=1.5 V and ICQ=2.85 mA 𝑅𝐸= 1.5 𝑉
2.85 𝑚𝐴 = 0.5 𝑘Ω
The collector current is related to other parameters of the circuit as seen in Equation (2).
𝐼𝐶=𝑉𝐶𝐶−𝑉𝐶𝐸
𝑅𝐶+𝑅𝐸 (2) Given IC to be 2.85 mA, VCC and VCE are 15 and 8 volts respectively.
𝑅𝐶+ 𝑅𝐸= 2.45 𝑘Ω
Haven gotten the RE in (1), therefore 𝑅𝐶 = 1.95 𝑘Ω
According to [15] when designing a circuit, standard components values must be chosen for actual realization.
Hence, the value of RC will be approximated to 2 kΩ. Since the emitter collector voltage (VCE) has a maximum value of 10 V, Equation (2) is utilized to obtain the minimum IC and denoted as 𝐼𝐶1
𝐼𝐶1= 15−10
2.45×103= 2.04 𝑚𝐴
According to [6], stability factor is expressed mathematically in Equation (3) as:
𝑆𝑒2 =∆𝐼𝐶
𝐼𝐶1×𝛽1
∆𝛽 (3) Change in collector current (∆IC)=0.81, minimum value of β1 =50, change in β1 (∆β) =250, minimum value of collector current (𝐼𝐶1) = 2.04. To obtain the stability factor (𝑆𝑒2), the values of ∆IC, β1, ∆β and IC1 are substituted. This yields a stability factor of 0.0794. Therefore, from the known value of 𝑆𝑒2, the base resistance (RB) is obtained using Equation (4).
𝑆𝑒2 =
1+𝑅𝐸 𝑅𝐵
1+(1+𝛽𝑓)𝑅𝐸⁄𝑅𝐵 (4) When the values of 𝑆𝑒2 = 0.0794, RE = 0.5 and 𝛽𝑓=100 are substituted in Equation (4), yields 𝑅𝐵 = 3.81 𝑘Ω.
The voltage divider for the circuit can be designed using values for IC = 2.85 mA, 𝛽𝑓 =100 and RE = 0.5 kΩ.
Furthermore, the collector current IC may be expressed as Equation (5)
𝐼𝐶=𝛽𝑓(𝑉𝐵𝐵−𝑉𝐵𝐸)
𝑅𝐵+(𝛽𝑓+1)𝑅𝐸 (5) Making VBB-VBE the subject of the formula in Equation (5), we obtain that
(𝑉𝐵𝐵− 𝑉𝐵𝐸) =𝐼𝐶(𝑅𝐵+(𝛽𝑓+1)𝑅𝐸)
𝛽𝑓 Where VBB-VBE= 1.547 V
Hence, to obtain base bias voltage VBB, we recall that VBE= 0.7 V. Therefore, 𝑉𝐵𝐵 = 2.247 𝑉.
Equations (6) and (7) are used to obtain values of the biasing resistors 𝑅1 and 𝑅2.
𝑅1= 𝑅𝐵(𝑉𝐶𝐶
𝑉𝐵𝐵) (6)
𝑅1 = 3.81 ( 15
2.247) = 25.4 𝑘Ω Furthermore, we have (𝑉𝐶𝐶
𝑉𝐵𝐵) = 1 + (𝑅1
𝑅2) (7) Hence, 𝑅2= 4.47 𝑘Ω.
The base current (IB) is evaluated using the Equation (8) 𝐼𝐶 = 𝛽𝐹𝐼𝐵 (8)
B. Design Method for the Multistage CE Amplifier The multistage amplifier circuit involves more than one amplification stage; therefore the design of the first stage is obtained which entailed determination of values of passive components R1, R2, R3, R4, RE and RC. These values form the basis as they are replicated to form the second stage of the amplifier circuit still maintaining the same n-p-n transistor type 2N2222 as shown in Fig. 2.
Fig. 2. A multistage CE amplifier configuration design
The DC equivalent circuit of the multistage amplifier stage is obtained by opening all capacitors and shorting all input sources for all stages. The multistage amplifier uses a voltage divider biasing method; Biasing resistances are designed to make the transistor operate in the active region.
Fig. 3 shows the DC equivalent circuit for the multistage CE amplifier.
Once a design has been completed, it should be checked to confirm that mathematical errors were not made. To check the design, it is important to calculate the expected Q point values using the calculated resistor values.
Fig. 3. DC equivalent circuit for a multistage CE amplifier
C. AC Analysis for Single Stage CE Amplifier
The AC equivalent circuit is obtained by shorting all capacitors and grounding the DC supply voltage and replacing the transistor with its hybrid model. There are
various methods of performing the AC analysis, but this work focuses on the use of a hybrid model of analysis, which would entail using hybrid parameters such as input impedance (
h
ie), output impedance (hoe), reverse voltage gain (hre) and forward current gain (hfe), to find transistor parameters such as current gain, voltage gain and power gain. While the values of (h
ie), (hoe), (hre) and (hfe) are obtained from transistor 2N2222 datasheet (hfe)= 100, (hoe)=25 uA , (hre)=
h
=2.5e-3 and (h
ie)=1.1 kΩAccording to [6], [16] and [17], the analysis follows the succeeding pattern; Fig. 4 depicts the AC equivalent circuit of the first stage of the CE amplifier circuit using values previously established.
Fig. 4. AC equivalent circuit of the first stage of CE amplifier
The current gain Ai of the first stage of the amplifier circuit is given by evaluating Equation (9).
𝐴𝑖= − 𝐻𝑓𝑒
1+ℎ𝑜𝑒𝑅𝐿 (9) Where, 𝑅𝐿 is the load resistance.
Substituting values of (hfe) (hoe), and RL, the current gain equals -95.25. The input resistance of the transistor looking directly into the base is defined by the relation in (10)
𝑅𝑖= ℎ𝑖𝑒+ ℎ𝑟𝑒𝐴𝑖𝑅𝐿 (10) Substituting the values of hie, hre, Ai and RL in Equation (10) yields Ri = 623.85 Ω.
Since the circuit has base resistors, therefore the stage input resistance denoted by Ris is given by the expression in Equation (11) as
𝑅𝑖𝑠= 𝑅1//ℎ𝑖𝑒 (11) Substituting the values of Ri and hie yeilds Ris=535 Ω. The output Resistance R0, evaluated from Equation (12) given that RL=RC=2 kΩ is
𝑅0= 1
ℎ𝑜𝑒//𝑅𝐿 (12) The voltage gain of the first stage of the amplifier is expressed in Equation (13) and the negative sign in the equation indicates that the output is out of phase in relation to the input signal.
𝐴𝑉= − ℎ𝑓𝑒𝑅𝐿
ℎ𝑖𝑒+∆ℎ𝑅𝐿 (13) Substituting values hfe=25 μA, RL=2 kΩ, hie=1.1 kΩ,
∆h=2.5 × 10−3 into Equation (13) gives AV=-180. There is a need to also calculate for the power gain, which is a product of voltage and current gains as shown in (14).
𝐴𝑃= 𝐴𝑉𝐴𝑖 (14)
Substituting values of AV=95 and Ai=180 in Equation (14) gives
𝐴𝑃= 95 × 180 = 17100
D. AC Analysis for Second Stage of the CE Amplifier
Fig. 5: AC equivalent circuit showing the output of first stage and the second stage of the CE amplifier
Fig. 5 shows the output of the first stage and the input to the second stage of the CE amplifier circuit when examined using the AC analysis. To perform the analysis for the second stage, there is a need to calculate various current values. To include the effective value of the source current which is denoted by IS, and expressed as Equation (15)
𝐼𝑠= 𝑉𝑠
𝑅𝑖𝑠 (15) where VS and IS are source voltage and current respectively. Hence, 𝐼𝑠=0.01
535 = 18.6 𝜇𝐴
Equation (16) provides an expression for the effective collector current (Ice)
𝐼𝑐𝑒 = 1/ℎ𝑜𝑒
1 ℎ⁄ 𝑜𝑒+𝑅𝐿 (16) Substituting values of hoe=25 μA, RL=2 kΩ and IC=2.85 mA in Equation (16) gives Ice=2.71 mA.
The signal input current to the second stage is denoted (IS2), the value is found by applying the current divider rule, using the output resistance (R0), input resistance (Ri) and collector current (Ic)
𝐿𝑆2= 𝑅0
𝑅0+𝑅𝑖𝑠(𝐼𝐶) (17) Substituting values R0=2kΩ, RIS =535Ω and IC=2.85 mA in (17) gives Is2=2.22 mA.
To obtain the current amplification as it appears at the output circuit of the second stage, there is need for base current of the second transistor, using current divider rule;
𝐿𝐵2 = 𝑅𝐵
𝑅𝐵+ℎ𝑖𝑒(𝐼𝑆2) (18) Substituting the values for RB=3.81 kΩ, hie =1.1 kΩ and IS2=2.22 mA into the Equation (18) gives IB2=1.72 mA.
Where, IB2 = Base current for second stage.
The current source 𝐼𝐶𝑜𝑢𝑡2 at the output of the second stage is:
𝐼𝐶𝑜𝑢𝑡2= ℎ𝑓𝑒𝐼𝐵2 (19) Hence, solving for 𝐼𝐶𝑜𝑢𝑡2 yields a value of 0.172 A.
The current gain of the second stage of the amplifier in
Fig. 5 may be calculated using Equation (20), 𝐴𝑖2=𝐼𝑆2
𝐼𝑆1 (20) Where IS1, IS2 are the respective source currents for the first and second stages of the amplifier.
Therefore, 𝐴𝑖2=2.22 𝑚𝐴
18.6 𝜇𝐴 = 119
Also, the total current gain is evaluated in Equation (21) 𝐴𝑖𝑇= 𝐴𝑖1× 𝐴𝑖2 (21) where 𝐴𝑖𝑇 is the total current gain
𝐴𝑖𝑇 = 95 × 119 = 11305
The total output gain of the two stage common emitter amplifier is given by Equation (22).
𝐴0𝑇 =𝐼𝐶𝑄𝑅𝐶2
𝑉𝑆 (22) Where 𝐴0𝑇 is the total output gain.
Substituting 𝐼𝐶𝑄=2.85 mA, 𝑅𝐶2=2 kΩ and 𝑉𝑆= 10 mV gives:
𝐴0𝑇=2.85 × 10−3× 2 × 103 10 × 10−3 = 510
Also, the power gain is a product of current and voltage gains, given by the Equation (23)
𝐴𝑝= 𝐴𝑖× 𝐴𝑉 (23) Substituting values of AI=11305 and AV=510 gives:
AP = 11305 × 510 = 5765550
IV. RESULTS AND DISCUSSION
After the analytical method was used to calculate the parameters of the amplifier, the designed circuits were simulated with LT SPICE. The LT SPICE representation of the designed single stage and multistage CE amplifiers are shown in Fig. 6 and Fig. 7 respectively.
Fig. 6. SPICE representation of the designed single stage CE amplifier
Fig. 7. LT SPICE representation of the designed multistage CE amplifier
Component values: R1=25 kΩ, R2=4 kΩ, RE=0.5 kΩ, RC=2 kΩ, C1= C3=1 μF and C4=100 μF were obtained.
Figs. 8 and 9 show simulation results for alternating current (AC) analyses of both single- and multi- stage CE amplifier with gains of 45 dB and 55 dB respectively.
Parameters estimated both manually and through simulation are presented in Tables II and III for easy comparison.
Fig. 8. Simulation result for AC analysis of single stage CE amplifier showing gain of 45 dB
Table II shows a comparison of the single stage result obtained from hand calculation and that obtained from LT SPICE.
TABLEII:SINGLE STAGE CEAMPLIFIER RESULT
Variable AC Analysis
Symbol AC in dB
Manually Estimated Value 20 log 180 = 45.10 𝑑𝐵
Simulated Value 20 log 172 = 44.71 𝑑𝐵
Fig. 9. AC analysis of the two stage CE amplifier showing gain of 55 dB
Table III shows a comparison of the multistage result obtained from hand calculation and that obtained from LT SPICE.
TABLEIII:MULTISTAGE CEAMPLIFIER RESULT
Variable AC Analysis
Symbol AC in dB
Manually Estimated Value 20 log 510 = 54.15 𝑑𝐵
Simulated Value 20 log 550 = 54.80 𝑑𝐵
V. CONCLUSION
The design and analysis of a multistage CE amplifier for low frequency applications has been presented in this research work. Using analytical method, voltage gains of 45 and 54 decibels were obtained for the single stage and multistage amplifiers respectively. The LT SPICE simulation software yielded 44 dB for the single stage and 54 dB for the multistage. The result of the multistage amplifier shows improved voltage and power gains over the single stage CE amplifier. The multistage CE amplifier is suitable for low frequency applications, and the hybrid model used in the analytical method is effective for analysis of the CE amplifier. LT SPICE simulation tool is promising and effective in analyses. The results obtained from the AC analysis and transient tests using simulation can be seen to be of reasonable agreement with the manually computed values for the gains.
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Dan Dan-Abia obtained his B.Eng. in Electrical and Electronic Engineering from Landmark University, Kwara State, Nigeria in 2015. He received a M.Eng degree in Electrical/Electronic Engineering with specialty in Electronics and Communications, from the University of Uyo, Uyo Akwa Ibom State Nigeria in 2019.
His research interests are in antenna design and also in amplifier designs, with special interest in analysis of multistage CE amplifiers.
Dan Dan-Abia is a Member of the Nigerian Society of Engineers (NSE).
F Akaninyene Obot obtained his B.Eng. in Electrical and Electronic Engineering from the University of Port Harcourt, Rivers State Nigeria in 1998. He received a M.Eng degree in Communications Engineering from Enugu State University of Science and Technology, Enugu Enugu State Nigeria in 2007. He obtained his PhD in Electrical Electronic Engineering with a core specialty in Communications Engineering from the University of Uyo, Uyo Akwa Ibom State Nigeria in 2016.
Dr. Obot is a senior lecturer with the Department of Electrical/Electronic and Computer Engineering, University of Uyo, Nigeria where he teaches both undergraduate and postgraduate students. His research interests are in radar systems, microwave and antenna Engineering, satellite communications, network analysis and synthesis, cellular mobile network and operations research. He has published several articles in both local and international journals.
Dr. Obot is a Member of the Nigerian Society of Engineers (NSE), and a Registered member of the Council for the Regulation of Engineering in Nigeria (COREN).
Kufre Udofia obtained his B.Sc. in Physics from University of Uyo, Nigeria in 2001. He received a M.Sc. degree in Mechatronic Systems Engineering from Lancaster University, Lancaster, United Kingdom in 2005, and also a M.Sc. in Electronic Mobile Communications in 2006 from the University of South Wales, Pontypridd, United Kingdom. He earned his PhD in Satellite Communications from the University of South Wales in 2011. He obtained a postgraduate diploma in Electrical and Electronic Engineering (PgD. Eng) from the Michael Okpara University of Agriculture Umudike, Abia State, Nigeria.
Dr. Udofia is now with the Department of Electrical/Electronic and Computer Engineering, University of Uyo, Nigeria where he lectures both undergraduate and postgraduate students. His research interests are in antennas and propagation, millimetre wave propagation involving satellite communications at varying radio frequency spectra, with special interest in fade mitigation techniques where he has published several papers.
Dr. Udofia is a Member of the Nigerian Society of Engineers (NSE), Institution of Engineering Technology (THEIET), Institute of Electrical and Electronic Engineering (IEEE), and the Royal Institute of Physics (IOP).
