THIRD YEAR LABORATORYSEE3732

SESION 2010/2011 SEMESTER 1

BASIC ELECTRONICS LABTORARY

LONG REPORT: AMPLIFIER FREQUENCY RESPONSE (BJT)

NAME : MUHAMMAD SAUKANI BIN ABDUL HALIM AZIZI

IC : 881230085891

MATRIX NO : BE090138

COURSE : 3SEC

SECTION : 8

GROUP : 15

GROUP MEMBER: WONG KING KIAT & LIEW SHAN SUNG

SUPERVISOR : DR. RUBITA SUDIRMAN

DATE : 23 SEPTEMBER 2010

TITLE :AMPLIFIER FREQUENCY RESPONSE (BJT)

Title: Amplifier Frequency Response (BJT)

Objectives 1. To obtain the frequency response of a BJT amplifier circuit.2. To determine the lower cutoff frequency and the upper cutoff frequency of a BJT

amplifier circuit.3. To determine the midband gain, Amid of a BJT amplifier circuit.4. To determine the input resistance, rin and the output resistance, ro of a BJT amplifier

circuit.

List of ApparatusComponents1. Transistor: BC109 (or equivalent general purpose npn)2. Resistor: 150kΩ, 33kΩ, 4.7kΩ, 680Ω(2)3. Capacitor: 0.22μF (2), 0.047μF, 470μF, 0.01μF(2)

Equipments1. Power Supply (TW63414)2. Oscilloscope (B019785)3. Function Generator (4020024535)4. Digital Multimeter (3146A25078)

Power Supply

Oscilloscope

Function Generator

Digital Multimeter

Amid3dB

fL fH

High-frequency rangeMidbandLow-frequency range

f(Hz)

Frequency response of a practical amplifier

Introduction

The input frequency of an amplifier is not only one fixed frequency; it can be in a range from low to high frequency. The ideal amplifier is supposed to operate at all frequency with the same output gain. The input resistance, rin and the output resistance, ro of an ideal amplifier will not change with input frequency. The phase different between input and output of an ideal amplifier will not be affected by frequency changes.

Practical amplifiers do not exhibit the features of the ideal amplifier because of the coupling and bypass capacitor effect in low frequency range, and stray capacitance and transistor capacitance effects in high frequency range. The midband range is the region where coupling and bypass capacitors act as short circuits, and stray and transistor capacitances act as open circuits. In this region, the gain is almost a constant. The gain at f=fL and at f=fH is 3dB less than the maximum midband gain. The bandwidth of the amplifier (in Hz) is defined as fBW=fH-fL.

The frequency response begins with the low-frequency range designated between 0Hz and lower cutoff frequency. The output gain is equal to 0.707Amid, where Amid is the constant midband gain. The higher frequency range covers frequency between upper cutoff frequency and above. The output gain at fH is similarly 0.707Amid. The gain increase in low-frequency range until the maximum value in minband frequency and decrease in high-frequency range which dies off eventually.

Av(dB)

The Lower Frequency Response

The reactance of capacitor, X

C= 1

2 π fC . The impedance of coupling and bypass capacitor decrease as the frequency increase. Thus the voltage gain of BJT amplifier increase as the frequency increase. At very low frequencies, the capacitive reactance may become large enough to drop some of the input voltage and output voltage. Also the emitter-bypass capacitor may no longer short the emitter resistor to ground. The following equation can be use to approximate the lower-cutoff frequency of the amplifier.

f 1=1

2πrin C1

where, f1 = lower cutoff frequency due to C1

C1=input coupling capacitance (C11//C12)rin=input resistance of the amplifier

f 2=1

2 πr oC2

where, f2 = lower cutoff frequency due to C2

C2=output coupling capacitancero=output resistance of the amplifier

f1 and f2 are not close in value. The actual lower cutoff frequency is approximately the larger frequency.

The Midband Response

In this range all capacitors are assumed to have very small effect on the circuit. Capacitors are considered as short circuit or no voltage drop over them. Stray and transistor capacitive reactance is still at a very large value and considered to be open circuit. Hence, the gain in this range will be constant and not affected by frequency changes. The gain in midband is the largest and is known as Amid.

The Upper Frequency Response

The capacitive reactance of a capacitor decrease as frequency increase. This can lead to problems for amplifiers used for high-frequency amplification. Transistor has inherent shunt capacitances between each pair of terminals. These capacitances effectively short the ac signal voltage

For the circuit in Figure 2, the upper cutoff frequency, fH due to shunt capacitor CB and feedback capacitance CC, can be closely approximate using the following general equations:

f H= 11

f 'A

+1

f 'B where,

f ' A=1

2πr s C ' A and f 'B=

12πrO CB

where, CA and CB are modified by adding the Miller-effect capacitance, which is the interelectrode feedback capacitance CCB modified by the gain Amid as follows:

C’A = CA + (1-Amid) CC , C’B = CB + (1-1/Amid)CC

where, Amid = the voltage gain from input-to-load midband.

However, capacitor Cp11 and Cp12 are used to subdue these shunt capacitance effects.So, fH can be evaluate approximately by

f 'H= 12 πr OC p '

where, Cp’ =Cp11//Cp12

Signals lost through transistor capacitances Part of signals lost

through stray capacitances

Method

Preliminary work1. Simulated frequency response, voltage gain versus frequency of the amplifier circuit given

in figure 2 was produced using MULTISIM or any equivalent software.2. The response was printed, and observed to determine the midband gain, Amid, lower cutoff

frequency, fL and upper cutoff frequency, fH. All value was recorded.

Experimental procedure1. Apparatus and all necessary connections was setup to carry out the required experimental

work in determining the frequency response of the amplifier circuit as shown in figure 2.2. Voltage was applied to the circuit. The base, the collector and the emitter voltage of the

transistor was measured and recorded.3. A sinusoidal input signal, Vi, with voltage of 1volt peak-to-peak value at frequency 5Hz

was applied to test the circuit.4. The output voltage, Vo was measured, recorded and the Av=Vo/Vi was calculated. The

phase different between input and output signals were also measured and record in the table.

5. The signal frequency was increased with the input signal always constant to get another set of output voltage, Vo, voltage gain and signals phase difference.

6. A frequency response table was created to tabulate the readings with frequency, input voltage, output voltage, voltage gain, phase difference, and the phase angle.

7. All necessary readings to cover frequency band between 5Hz and 50 kHz was produced. The input voltage was maintained constant.

8. The frequency response of (i) voltage gain in dB versus frequency, and (ii) phase response versus frequency was plotted on a semi-log paper.

Figure2: Amplifier circuit for the frequency response experiment

Results

Preliminary work (simulation) results

Mid band gain, Amid = 16.406dB

Lower cutoff frequency, fL =28.066 Hz

Upper cutoff frequency, fH =16.41 kHz

Experimental results

A. Transistor Measured Voltages

βfor transistor assumed to be 275

VB VC VE IC (calculated) IB (calculated)2.059V 7.04V 1.445V 1.0553mA 5.2127μA

B. Frequency Response TableFreq(Hz) Vi(peak-

peak)(V)Vo(peak-peak)(V)

Av=Vo/Vi(V)

Av(dB)=20logvo/vi

θ(phase difference)

Phase angle=180°+θ

5 0.97 1.36 1.4021 2.9353 82.21 262.218 0.98 2.04 2.0816 6.3681 75.69 255.6910 0.97 2.54 2.6186 8.3612 69.47 249.4715 0.97 3.40 3.5052 10.8941 58.06 238.0620 0.97 4.04 4.1649 12.3922 48080 228.8030 0.99 4.84 4.8889 13.7846 38.94 218.9440 0.97 5.28 5.4433 14.7172 28.78 208.7850 0.98 5.50 5.6122 14.9827 23.66 203.6660 0.98 5.60 5.7143 15.1392 21.74 201.74 70 0.99 5.72 5.7778 15.2353 19.14 199.1480 0.97 5.84 6.0206 15.5928 16.37 196.3790 0.97 5.86 6.0412 15.6225 11.99 199.99100 0.97 5.88 6.0619 15.6521 9.329 189.33200 0.97 6.06 6.2474 15.9140 4.520 184.52300 0.98 6.06 6.1837 15.8249 2.560 182.56400 0.97 6.10 6.2887 15.9712 0.920 180.92500 0.99 6.12 6.1818 15.8220 -1.188 178.81600 0.99 6.12 6.3093 15.9996 -1.020 178.98700 0.98 6.10 6.2245 15.8821 -2.269 177.73800 1.01 6.12 6.0594 15.6486 -1.674 178.32900 1.00 6.12 6.1200 15.7350 -3.059 176.941000 1.02 6.14 6.0196 15.5914 -4.899 175.102000 0.99 6.06 6.1212 15.7367 -8.064 171.933000 1.00 6.06 6.0600 15.6495 -10.42 169.584000 0.98 6.02 6.1429 15.7674 -12.19 167.815000 1.02 5.94 5.8235 15.3037 -16.23 163.7710000 1.04 5.38 5.1731 14.2750 -32.23 147.7715000 1.01 4.68 4.6337 13.3185 -44.05 135.9518000 1.02 4.30 4.2157 12.4974 -43.75 136.2524000 1.02 3.64 3.5686 11.6500 -56.87 123.1327000 1.03 3.45 3.3592 10.5348 -56.42 123.5830000 1.02 3.16 3.0980 9.8217 -65.66 114.3440000 1.03 2.60 2.5243 8.0427 -65.51 114.4945000 1.03 2.22 2.1553 6.6703 -68.23 111.7750000 1.05 2.18 2.0762 6.3453 -68.99 111.01

Graph of frequency response Plotted using Microsoft Excel

1 10 100 1000 10000 1000000

2

4

6

8

10

12

14

16

18 Frequency Response

Frequency (Hz)

Av (d

B)

1 10 100 1000 10000 1000000

50

100

150

200

250

300

Phase Angel vs frequency

Frequency (Hz)

Phas

e An

gel (

degr

ee)

C. Measured Frequency Response Parameters (from the plotted graph)

Lower cutoff frequency, fL =28 Hz

Midband gain, Amid =15.9 dBUpper cutoff frequency, fH =16 kHzPhase angle at lower cutoff frequency =217.5°Phase angle at midband frequency =175°Phase angle at upper cutoff frequency =135°

Question and Discussion

1. What are the simulated values of fL, Amid and fH for the common-emitter amplifier infigure 2? Compare these values with the cutoff frequencies obtained from themeasured values -The simulated values of fl ,Amid and fh for common-emmiter amplifier are 25.632 Hz, 16.391 dB and 17.564 kHz respectively, meanwhile the measured values of fl, Amid and fh from the expirement are ,28 Hz,15.9 dB and 16 kHz.- By comparing these two set of data , it is observed that the measured on reading values are generally different than simulated results with percentage error for fl is 9.23% ,Av is 8.49% and fh is 8.88% .This may due to the instrumentation error in adjusting the precise values of Vc and input frequency as well as internal capacitance and resistance of the amplifier circuit

2. Which capacitor affects on the lower cutoff frequency and the upper cutofffrequency of the amplifier circuit?-Coupling capacitor (C11 and C12 ) and bypass capacitor (CE) affects on the lower cutoff frequency-Cp11 and Cp12, stray capacitor (wiring)and transistor terminal capacitance affects on the upper cutoff frequency.

3. With cutoff frequencies known, find the input resistance, rin, and the outputresistance, rO , of the amplifier circuit

ri calculated using simulation result:

f L=12πri C1

=12 πri C11 // C12

=12 πri(0 . 22 μ // 0 . 047 μ)

25 . 632 Hz=12πri (0 .22 μ // 0 .047 μ )

ri=23 .255 kΩ

ri calculated using experimental result:

f L=12πri C1

=12 πri C11 // C12

=12 πri(0 . 22 // 0 . 047 μ )

28 Hz=12 πri(0 . 22 // 0 .047 μ )

ri=21. 2888 k Ω

ro calculated using simulation result:

f H=12 πro C P '

=12 πr o(C11 // C12 )

=12 πr o(0 .001 // 0 .001 μ )

17 . 564 kHz=12πr o(0 . 001 μ // 0. 001 μ)

ro=4 . 5307k Ω

ro calculated using experimental result:

f H=12 πro C P '

=12 πr o(C11 // C12 )

=12 πr o(0 .001 μ // 0. 001 μ)

16 kHz=12 πro (0.001 // 0 . 001 μ )

ro=4 . 9736k Ω

4. Obtain the empirical function to describe the measured frequency response of theamplifier circuit?-From the graph plotted ,the gain will drop 20 dB for eery decrease in frequency until the gain approachs zero. If the frequency drop in a factord of 2 ( (octave), the gain will drop dy 6 dB. The same thing happens for frequency higher than fh, whereby the gain drops by 20 dB per decade for the increase of frequency.- For midband frequency, the graphhremains constan without being affected by frequency changes-Also , by reffering to the graph plotted , the output signalis anti phase (in difference of 180°) to the input signalat midband frequency. The phase angle is decresing from lower to higher frequency.

5. Discuss your observation on the simulated and the measured frequency response- The measured results which obtain from the plotted graph are slightly different from the simulated results. This due to the errors from the instruments, environment and human. The instrument errors are due to the precision of value measured and supplies by the instrument. (Example: function generator and oscilloscope). The environment error its mainly due to the environment temperature. The human error is due to the adjustment made by human on asserting the input value. By referring to the plotted graph, it is observed that the graph pattern not as smooth as the simulated graph. There are certain points which deviate from the actual graph pattern. Thus, the values of Amid , fl and fh are different from the simulated results.

Conclusion

The frequency response of a BJT amplifier circuits can be obtained through two method: by simulation and by experiment. The simulation of the BJT amplifier circuit is done by using Multism Software , meanwhile the measured values of frequency response for BJT amplifier circuit is obtained by measuring and calculating the amplifier gain for a specific frequency range, which is later plotted as bode plot to simplify the analysis of frequency response of Bjt amplifier circuit.

The lower cutoff frequency and the upper cutoff of BJT amplifier circuit are determined by determining the values of Amid first and later find the frequency when the amplifier gain is 0.707 Amid. The smaller values of the respective frequencies obtained is the lower cutoff frequency meanwhile the another would be upper cutoff frequency.

The midband gain, Amid of the BJT amplifier circuit is determinedby taking the highest values of amplifier gain for a specified frequency range applied to the amplifier circuit.

The input resistance, ri of the BJT amplifier circuit is calculated by using the following equation:

f L=1

2 πri C1

= 12πr iC11 // C12

Where fl = lower cutoff frequency C11,C12 =coupling capacitor

The output resistance ,ro of the BJT amplifier circuit is calculated by using the following equation

f H= 12πr oCP '

= 12 πro (C11 // C12)

Where fh = upper cutoff frequency Cp11,Cp12=capacitor connected parallel to the output terminal

References

Siti Hawa Ruslan, Puspa Inayat Khalid, Ismawati Abdul Ghani (2003): Elektronik 2 Modul

Pengajaran Edisi ke-3, FKE UTM.