Lab 14 RS

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The Common Emitter Amplifier

Circuit

Construct the common emitter amplifier circuit below according to your type of emitter.

Calculate all the R and C values to use in the circuit such that

a. Try [math]\displaystyle{ R_B \approx 220 \Omega }[/math] and [math]\displaystyle{ I_C \approx 100 \mu A }[/math]

b. [math]\displaystyle{ I_C > 0.5 }[/math] mA DC with no input signal

c. [math]\displaystyle{ V_{CE} \approx V_{CC}/2 > 2 }[/math] V

d. [math]\displaystyle{ V_{CC} < V_{CE}(max) }[/math] to prevent burnout

e. [math]\displaystyle{ V_{BE} \approx 0.6 V }[/math]

f. [math]\displaystyle{ I_D \approx 10 I_B < 1 }[/math] mA

Let's [math]\displaystyle{ V_{CC} = 11\ V }[/math], [math]\displaystyle{ R_E = 0.2\ k\Omega }[/math] and [math]\displaystyle{ R_C = 2.0\ k\Omega }[/math].

The load line equation becomes:

[math]\displaystyle{ I_C = \frac{V_{CC}-V_{CE}}{R_E+R_C} = \frac{(11 - V_{CE})\ V}{2.2\ k\Omega}  }[/math]

Draw a load line using the [math]\displaystyle{ I_{C} }[/math] -vs- [math]\displaystyle{ I_{EC} }[/math] from the previous lab 13. Record the value of [math]\displaystyle{ h_{FE} }[/math] or [math]\displaystyle{ \beta }[/math].

On the plot below I overlay the output transistor lines (from the previous lab report #13) and the Load Line calculated above.

My reported values of [math]\displaystyle{ \beta }[/math] in lab report #13 was [math]\displaystyle{ \beta \approx 150 }[/math]. But this because we have used the approximation [math]\displaystyle{ V_E \approx 0 }[/math] because small resistor value [math]\displaystyle{ R_E = 100\ \Omega }[/math] was used.

If we will do the accurate calculation of [math]\displaystyle{ \beta }[/math] based on my lab report #13 measurements using exact formula:

[math]\displaystyle{ I_B = \frac{(V_{bb}-V_{BE}-V_E)}{R_B} }[/math]

we will end up with value of [math]\displaystyle{ \beta }[/math]:

 [math]\displaystyle{ \beta \approx 170 }[/math]

Set a DC operating point [math]\displaystyle{ I^{\prime}_C }[/math] so it will amplify the input pulse given to you. Some of you will have sinusoidal pulses others will have positive or negative only pulses.

I will set up my operating point in the middle of the load line:

[math]\displaystyle{ I_C = 2.5\ mA }[/math], [math]\displaystyle{ V_{EC} = 5.5\ V }[/math].

Let's calculate all bias voltage needed to set up this operating point. Because the knowing of [math]\displaystyle{ V_{BE} }[/math] and [math]\displaystyle{ \beta }[/math] is very important for this calculation I did the preliminary set up to measure this quantities. They are the only parameters which depends from transistor. I was able to find:

[math]\displaystyle{ V_{BE} = 0.68\ V }[/math]

[math]\displaystyle{ \beta = 173 }[/math]

Now

[math]\displaystyle{ V_E = I_E \cdot R_E = 2.5\ mA \cdot 0.2\ k\Omega = 0.5\ V }[/math]
[math]\displaystyle{ V_B = V_E + V_B = (0.50 + 0.68)\ V = 1.18\ V }[/math]

To set up the above operating point we need to set up [math]\displaystyle{ V_{B} = 1.18\ V }[/math].

We have:

[math]\displaystyle{ I_B = \frac{I_C}{\beta} = \frac{2.5\ mA}{173} = 14.4\ uA }[/math].

To get operating point independent of the transistor base current we want [math]\displaystyle{ I_{R1} \gg\ I_B }[/math]

Let's [math]\displaystyle{ I_{R1} = 590\ uA \gg\ I_B = 14.4\ uA }[/math]

So

[math]\displaystyle{ R_1 = \frac{V_B}{I_1} = \frac{1.18\ V}{590\ uA} = 2\ k\Omega }[/math]

And [math]\displaystyle{ R_2 }[/math] we can find from Kirchhoff Voltage Low:

[math]\displaystyle{ V_{CC} = I_2 \cdot R_2 + V_B }[/math].

and Kirchhoff Current Low:

[math]\displaystyle{ I_2 = I_1 + I_B }[/math]

So

 [math]\displaystyle{ R_2 = \frac{V_{CC}-V_B}{I_1+I_B} = \frac{(11-1.18)\ V}{(590 + 14.4)\ mA} = 16.25\ k\Omega }[/math]

I tried to adjust my calculation by varying the fee parameters [math]\displaystyle{ V_{cc} }[/math] and [math]\displaystyle{ I_1 }[/math] to end up with all my resistor values I can easily set up.

Measure all DC voltages in the circuit and compare with the predicted values.(10 pnts)

My predicted DC voltages are: (from the calculation above):

[math]\displaystyle{ V_{EC} = 5.50\ V }[/math] 
[math]\displaystyle{ V_{BE} = 0.68\ V  }[/math]

[math]\displaystyle{ V_E = 0.50\ V }[/math]
[math]\displaystyle{ V_B = 1.18\ V }[/math]
[math]\displaystyle{ V_C = V_E + V_{EC} = (0.50 + 5.50)\ V = 6.00\ V }[/math]

My measured DC voltages are:

Here is very important to set up all resistor values as close as possible to my assumed values.

After many tries and errors I was able to end up with the following values of my resistors:

[math]\displaystyle{ R_E = (200.0 \pm 0.1)\ \Omega }[/math]
[math]\displaystyle{ R_C = (2.002 \pm 0.001)\ k\Omega }[/math]
[math]\displaystyle{ R_1 = (2.004 \pm 0.001)\ k\Omega }[/math]
[math]\displaystyle{ R_2 = (16.26 \pm 0.01)\ k\Omega }[/math]

And my measurements of DC voltages looks like:

[math]\displaystyle{ V_{cc} = (11.00 \pm 0.01)\ V }[/math]

[math]\displaystyle{ V_E = (0.500 \pm 0.001)\ V }[/math]
[math]\displaystyle{ V_B = (1.183 \pm 0.001)\ V  }[/math]
[math]\displaystyle{ V_C = (6.03 \pm 0.01)\ V  }[/math]

[math]\displaystyle{ V_{BE} = (0.683 \pm 0.001)\ V }[/math]
[math]\displaystyle{ V_{EC} = (5.53 \pm 0.01)\ V }[/math]

[math]\displaystyle{ V_{R_2} = (9.82 \pm 0.01)\ V }[/math]
[math]\displaystyle{ V_{R_C} = (4.97 \pm 0.01)\ V }[/math]

All my measurements are in agreement with each other within experimental errors.

I mean here that [math]\displaystyle{ V_B = V_E+V_{BE} }[/math], [math]\displaystyle{ V_C = V_E+V_{EC} }[/math] and [math]\displaystyle{ V_{cc} = V_B+V_{R_2} }[/math], [math]\displaystyle{ V_{cc} = V_C+V_{R_C} }[/math]

Also all my predicted values are in agreement with my measured DC voltage values except of the fact that my measured [math]\displaystyle{ V_{BE} = 0.683\ V }[/math] instead of [math]\displaystyle{ V_{BE} = 0.680\ V }[/math] as I initially assumed. That gives me the correspondent corrections to [math]\displaystyle{ V_B }[/math]. But if I will consider only the one significant sign all my predicted and measured DC voltage values are in total agreement.

Below are my current measurements which I did using millivoltmeter and which are also in agreement with each other and with all my previous calculation:

[math]\displaystyle{ I_E = (2.48 \pm 0.01)\ mA }[/math] 
[math]\displaystyle{ I_C = (2.49 \pm 0.01)\ mA }[/math] 
[math]\displaystyle{ I_B = (14.4 \pm 0.1)\ uA }[/math] 

[math]\displaystyle{ I_1 = (588 \pm 1)\ uA }[/math] 
[math]\displaystyle{ I_1 = (603 \pm 1)\ uA }[/math]

Measure the voltage gain [math]\displaystyle{ A_v }[/math] as a function of frequency and compare to the theoretical value.(10 pnts)

Measure [math]\displaystyle{ R_{in} }[/math] and [math]\displaystyle{ R_{out} }[/math] at about 1 kHz and compare to the theoretical value.(10 pnts)

How do you do this? Add resistor in front of [math]\displaystyle{ C_1 }[/math] which you vary to determine [math]\displaystyle{ R_{in} }[/math] and then do a similar thing for [math]\displaystyle{ R_{out} }[/math] except the variable reistor goes from [math]\displaystyle{ C_2 }[/math] to ground.

Input impedance [math]\displaystyle{ R_{in} }[/math] measurements

To measure the input impedance of my amplifier I have set up the circulant below. Here I have attached the resistor [math]\displaystyle{ R_L }[/math] in-front of capacitor [math]\displaystyle{ C_1 }[/math] and I replaced all my input internal resistor of amplifier by equivalent resistor [math]\displaystyle{ R_{inp} }[/math].

Using Ohm's Law:

[math]\displaystyle{ I = \frac{V_B-V_A}{R_L} }[/math]

and

[math]\displaystyle{ R_{inp} = \frac{V_B}{I} = R_L\ \frac{V_B}{V_B-V_A} }[/math]

Below is the table with my measurements and [math]\displaystyle{ R_{inp} }[/math] calculation. I did that calculation for several values of [math]\displaystyle{ R_L }[/math]

We can see that the input impedance of amplifier have small dependence from [math]\displaystyle{ R_L }[/math] because we change a little the base current.

Output impedance [math]\displaystyle{ R_{out} }[/math] measurements

To measure the output impedance of my amplifier I have set up the circulant below. Here I have attached the resistor [math]\displaystyle{ R_L }[/math] after of capacitor [math]\displaystyle{ C_2 }[/math] and I replaced all my output internal resistor of amplifier by equivalent resistor [math]\displaystyle{ R_{out} }[/math].

Here to find out the output impedance we can use the battery method from lab#1. By Kirchoff voltage law:

[math]\displaystyle{ V_B=V_A - I\cdot R_{out} }[/math]

and

[math]\displaystyle{ I = \frac{V_B}{R_L} }[/math]

So by graphing the current on the x-axis and the measured voltage [math]\displaystyle{ V_B }[/math] on the y-axis for several values of the resistance [math]\displaystyle{ R_L }[/math] we can find the output internal impedance of our amplifier as the slope of the line [math]\displaystyle{ V_B=V_A - I\cdot R_{out} }[/math]

Below is the table with my measurements and current calculation:

And below is my plot of output voltage [math]\displaystyle{ V_B }[/math] as function of current [math]\displaystyle{ I }[/math]:

The line equation is [math]\displaystyle{ V_B[mV]=p_0 + p_1\cdot I[\mu A] }[/math] The slope of this line is [math]\displaystyle{ p_0=(1.971\pm 0.004) \frac{mV}{\nu A} = (1.971\pm 0.004)\ k\Omega }[/math].

So the measured output impedance of my amplifier is output

[math]\displaystyle{  R_{out} = (1.971\pm 0.004)\ k\Omega }[/math]

Questions

1. Why does a flat load line produce a high voltage gain and a steep load line a high current gain? (10 pnts)
2. What would be a good operating point an an [math]\displaystyle{ npn }[/math] common emitter amplifier used to amplify negative pulses?(10 pnts)
3. What will the values of [math]\displaystyle{ V_C }[/math], [math]\displaystyle{ V_E }[/math] , and [math]\displaystyle{ I_C }[/math] be if the transistor burns out resulting in infinite resistance. Check with measurement.(10 pnts)
4. What will the values of [math]\displaystyle{ V_C }[/math], [math]\displaystyle{ V_E }[/math] , and [math]\displaystyle{ I_C }[/math] be if the transistor burns out resulting in near ZERO resistance (ie short). Check with measurement.(10 pnts)
5. Predict the change in the value of [math]\displaystyle{ R_{in} }[/math] if [math]\displaystyle{ I_D }[/math] is increased from 10 [math]\displaystyle{ I_B }[/math] to 50 [math]\displaystyle{ I_B }[/math](10 pnts)
6. Sketch the AC equivalent circuit of the common emitter amplifier.(10 pnts)

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