PROBLEM:
1.Find the Voltage drop at
a. Vb Voltage Bias
b. Ib Current
c. Ie Current
d. Ic Current
2.Find the Voltage Gain and r'e
3.Determine the resonant Frequency of the tank circuit Capacitors in Series
*Given:
Vcc= 28V
RC= 1kilo Ohm
RB1= 8.2 kilo Ohm
RB2= 1.5 Kilo Ohm
RE= 1.2 Kilo Ohm
Si= 0.7 Volts
*Equation:
(1. a)
by VDP Voltage Divider Principle
Vb = 28 Volts *(1.5 Kilo Ohm/ (1.5 Kilo Ohm + 8.2 Kilo Ohm))
Vb= 4.32 Volts approximately equal to The Simulated Value at Vb which is 4.29V
(1.b)
solving for Ib=?
Ib#1= (Vcc-Vb)/ 8.2 Kilo Ohm
Ib#1= 2.887mA approximately 2.89mA
Ib#2= 4.32Volts/1.5Kilo Ohm
Ib#2= 2.88mA
(1.c)
Solving for Ie=?
Ie= Vb - 0.7Volts / (1.2 Kilo Ohm )
Ie= 3.016mA approximately equal to the simulated value at 2.95mA
(1.d)
Vbe= Vb-Ve = 4.32V-(0.7)= 3.62V
Vcc-Vbe+(0.7)=Vc
Vc=28V- 3.62V+0.7V = 25.08Volts or approximately equal to 25.1 Volts
therefore:
Ic= Vcc-Vc/Rc = (28-25.1) Volts/1 Kilo Ohm
Ic= 2.9mA
2. Equation of Voltage Gain and r"e
Voltage gain denotes as AV where AV= Rc/Re
Therefore:
Av= Rc/Re = 1 Kilo Ohm/ 1.2 Kilo Ohm
Av=0.8333 (will not oscillate) because it is not greater than 1
Finding the r'e from the equation at room temperature:
r'e= 26mV/Ie
therefore:
r'e= 26mV/ 3.016mA
r'e=26mV / 3.016mA
r'e=8.62 ohm
plugging this value of r'e to the equation of Voltage Gain Av= Rc/r'e
Av= 1 Kilo Ohm/ 8.62 Ohm
Av= 116 ; Voltage gain with internal resistance in emmitter diode r'e
Therefore this Oscillator will Oscillate due to Av > 1
3. Determine the resonant Frequency of the tank circuit Capacitors in Series.
C1= 4.7 nano Farad C2= 47 nano Farad
Finding fr=1/2π(L Ctotal) ̂ 0.5
Where
Ct= C1*C2/C1+C2
Ct=4.27 nano farad, plug in this value to fr=1/2π(L Ctotal) ̂ 0.5 that gives resonant frequency
fr= 1/2π(L *4.27nF) ̂ 0.5 = 76.995Khz or 77Khz
*Follow this procedure below
* to see the signal waveform. Toggle the 2 switches from the 1 micro farad to the base of the transistor and the tank circuit to the collector side of the transistor for the feedback, then play the button and wait for 5 to 10 seconds before it appears.
* Observe the frequency that flashes on the simulation screen for about 1 to 2 minutes from a varying frequency of 73Khz to 74Khz.
* That gives you a slight and almost negligible difference of 2 to 3 KHz from the calculated value of resonating frequency (fr).
