# Transistor as an amplifier

I'm currently working on this circuit and it appears that my output voltage is not showing the correct values for the positive half wave .

For starters I have these values below - $$\U_{CE} = 5 V\$$

• $$\R_1 = 6.1kΩ\$$
• $$\ R_2 = 1.35kΩ\$$
• $$\ R_E = 1kΩ \$$
• $$\ R_3 = 1.5kΩ\$$
• $$\V_1 = 15 V \$$
• $$\ I_C = 2mA \$$
• $$\ U_{BE} = 0.4V \$$
• $$\ B = 180 \$$

Given formula $$\r_{BE} \approx \frac {40 mV}{I_B}\$$ First I calculated CE with the use of this formula $$\τE ≈ (r_{BE}·C_E ) / β = 1/(2 \pi f) \$$

These are my calculations:

$$I_C = B . I_B$$ $$rBE = 40mV/ I_B = 40mV . B / I_C = 40 . 180 / 2 mA ≈ 4kΩ$$

Let's say the frequency of this amplifier is 1kHz

$$=> τE = 1/(2 \pi f) = 1/(2 \pi 1000) = 1.519 . 10^{-4} s$$

Which makes

$$=> C_E = B.τE / rBE = 1.519.10^{-4} . 180 / 3600 = 7.6 uF$$

And also

$$τE = (r_E / B ). C1$$ $$τE = (R_E / B )* C1$$ $$r_E = (rBE + B Re) || R1 || R2 = (4kΩ + 180 * 1kΩ) || 6.1kΩ || 1.35kΩ = 1100 Ω = 1.1 kΩ$$

$$C1 = τE . B / r_E => C1 = ( 1.519 . 10^{-4} s . 180 ) / ( 1.1 * 10^{3} ) = 0.26 uF$$

Then with this question I could calculate C_2.

What is the minimum size of capacitor C2 if the lower limit frequency should be approx.imately 1000 Hz when the output is loaded with 100 kΩ?

$$τE = R * C2 => C2 = τE / R = 1.519 * 10^{-4} / 100kΩ = 1.519 nF$$

$$Ue =√( (1+ω²(R1*C1)²) * (1+ω²(R2*C2)²) . (1+ω²(RE*CE)² )) = 8.5 V$$

Summary :

• $$\C_E = 7.6 uF \$$
• $$\C_1 = 0.26 uF \$$
• $$\C_2 = 1.519 nF \$$

And with these calculations I can simulate my circuit .

Output in red, input in blue: Shouldn't the positive wave of the output voltage be bigger than the positive wave of the input voltage?

• You appear to be powering your circuit with AC from V1 -am I reading that correctly?
– Frog
Dec 28 '20 at 21:47
• Are you really using a sine wave source as the power supply? Dec 28 '20 at 21:47
• Sorry my bad . Forgot to change them . Just wanted to check the simulation with the sin waves Dec 28 '20 at 21:50
• Your input voltage is way, way too high. Dec 28 '20 at 21:56
• For an amplifier with relatively minimal feedback such as here, start with a small signal (millivolts). Larger signals will distort as g_m varies, even saturating as you see here. Dec 28 '20 at 22:07

Then I re-biased the transistor and reduced the level again. 