Design of a Single Transistor DC Current Source

Lab 4–Design of a Single Transistor DC Current Source

Perform lab in class during the week of Feb. 18-22, 2019

Group Lab Report  

Purpose:           To measure and analyze the characteristics of current sources.

To measure and analyze the characteristics of a voltage divider used for biasing transistor circuits.

Equipment:      Dual DC power supply

2N3904NPN transistor

To Be Determinedresistors

10 kW potentiometer

Two Digital Multimeters (DMM)

Breadboard

Wire Jumper Kit

Connecting leads

LED Collection

Problem Definition and Background Theory

Goal: Design a current source which provides a fixed DC current through a variable load resistance, R_L.  The current will remain fixed over a voltage range of 0 volts to some defined maximum DC voltage.

The basic layout of the Transistor Current Source Circuit is shown in Figure 1. The parameters are:

V_CC = DC power supply

R_L= Load resistance of the current source

V_L = DC load voltage

I_B = DC base current

I_C = DC collector current

I_E = DC emitter current

V_B = DC base voltage

V_C = DC collector voltage

V_E = DC emitter voltage

V_BE = DC base-emitter voltage

V_CE = DC collector-emitter voltage

In active operation, the transistor has the following properties:

V_BE = 0.7 volts and I_C =βI_B

where β is the DC current gain of the transistor.

Kirchhoff’s Current Law gives us several current equations:

I_E =I_B +I_C         I₁ =I_B +I₂

Kirchhoff’s Voltage Law gives us several voltage equations:

V_B =V_E  +V_BE            V_C =V_E  +V_CE        V_CC =V_L + V_C

Ohm’s Law gives us several resistor equations:

V_E =I_E R_E                                            V_L =I_C R_L         V_B =I₂ R₂

Power equations include:

P_T =V_CE I_C = power dissipated in the transistor in Watts

P_RE=V_E I_E = power dissipated in R_E in Watts

P_RL =V_L I_C= power dissipated in R_L in Watts

P_R1=(V_CC -V_B)I₁ = power dissipated in R₁ in Watts

P_R2 =V_B I₂ = power dissipated in R₂ in Watts

The equivalent resistance looking into the base is

The design process starts by choosing a DC fixed current for the current source and a DC voltage for the power supply, V_CC.  This fixed current value is the same as I_C , the DC collector current.

The design tasks are to:

• Derive values for R₁, R₂, R_E, to produce the desired fixed current value.

• Compute the transistor and resistor powers to make sure that the transistor and resistors can handle the power expected.

We begin by setting

(1)

This will produce a relatively low V_E, allowing for a wide range of V_L.  Next we calculate the emitter voltage from KVL:   V_E  =V_B -V_BE.

Assuming active operation, we have volts and

(2)

Substitute (1) into (2) to get:

(3)

Next we manipulate equation (3) and the KVL equations:

V_C =V_E  +V_CE                     V_CC =V_L + V_C                                                        (4)

to get:

(5)

Next we compute the maximum allowable load voltage.  This occurs when  is at a minimum value.   is minimized when the transistor is operating in the saturation region.  In the saturation region, both PN junctions are in forward mode and  volts.   To summarize, the maximum load voltage is:

where  volts.  We substitute  volts to get:

(6)

We now have a current source, equivalent to figure 2, in which the current is fixed at I_C as R_L changes.  This is a good thing.  Notice that we are allocated about 2/3 of V_CC as the range of .  This is also pretty decent.   As we increase R_L from 0 Ohms, the load voltage will change from 0 volts to  as defined in equation (6).

The maximum load resistance comes from Ohm’s Law:

(7)

Prelab – Design Calculations for the DC Current SourceName______________

1. (10 pts) Using the background information in part 1, and the approximation that , derive the following equation for as a function of ,  , and β.  Hint:  Substitute , and  into

2. Using the answer to question 1 and the background information in part 1, in which the base voltage is designed for , and is designed for , derive equations for
3. a) as a function of ,  , and β.

1. b) (10 pts) as a function of ,  , and β using .   The goal of a stable current source is to have a stable base voltage, in which the transistor does not load down the circuit.  If we remove the transistor, the base voltage should not change.  To do this, we set to target approximately a tolerance of 5%, we set .

1. c) as a function of ,  , and β.

3. (50 pts) Given the answers to question 2, design a 10 mA transistor current source with a supply voltage of volts, and β =150. Show all calculations for the following quantities:

P_T(max)          P_REP_RL(max)         P₁             P_R2

P_T(max) =maximum power dissipated in the transistor

P_RE= power dissipated in R_E

P_RL(max) =maximum power dissipated in R_L

P₁ =power dissipated in R₁

P_R2 =power dissipated in R₂

…and draw a schematic diagram of the final circuit with all currents and node voltages indicated on the sketch.

Lab Instructions

Team members:_________________________________

Part 1 – Construct Current Source Circuit

• □On the breadboard, construct the 10 mAvoltagedivider transistor circuit that you designed in the Pre-Lab.For this initial step, use a load resistor of RL= 0W.

With RL = 0 W, what should VC be?   ________

What should VB  be approximately?  ________  (refer to the prelab)

What should VE  be approximately?  ________  (refer to the prelab)

• □Turn on the power supply and set the voltage to 20 volts and observe the current value displayed on power supply. There should be a source current in the mA range.

If the source current is 1.000 Amps, then there is a short circuit connection… if the source current is 0.000 Amps, then there is an open circuit … In either case, turn off the power supply, debug the circuit, and try again.

When the source current is in the mA range, record the source current, measure the transistor voltages and record below:

Source current = __0.011A____________

VB = ___6.56V_______ ,      VC = ____19.8V______ ,      VE = ______5.83V____

• □Compare the measured VBand VEabove with your Prelab calculations.  They should differ by about 0.7 volts.  If they are way off, then you will need to debug the circuit.  Debugging tips:The high sides of RLand R1 should both be about 20 V.So you can use a DMM set up as a DC voltmeter to check these test points.   The low sides of R2and RE should be connected to ground, so the voltages at these points should both be 0 V.  You can use a voltmeter to check these test points.   If any of these four voltage test points are off, then there is probably a bad connection somewhere.  To find a bad connection, use the voltmeter to trace the faulty test point back to the power supply.  If this still does not help, then ask the instructor for assistance.
• □ Now that the circuit is operation properly, set up the DMM to measure collector current, IC.

Measured IC = ____9.52______ mA

What should IC be according to the prelab?   _____10_____ mA

• □Show the circuit to the instructor before continuing.

Instructor sign off: ____RDA 2/19/19__________

Part 2 – Testing of the Current Source

A current source should be able to deliver a fixed current over a range of load resistance.  In this section, the BJT current source is tested to determine the range of operation and % regulation of the current source.

• □Fill in Table 1 with measurements of VB, VE, VC, and ICfor values of VLranging from 0 to14 volts.  You will need to adjust the variable resistor to change the value of the load voltage. For the last row of table 1, adjust the variable resistor until the collector current drops to 9 mA.

Table 1 – Measured and Calculated Results of Current Source

Vc = Vcc-V_L

P_T = VCE * IC

VCE= VC – VE

• □ You should notice that the collector current (IC) remains fairly steady as RL(and VL) increases, but then at some point  IC drops significantly.  How high does VLget before the current start to drop significantly?

VLmax (experimental)= _____14____.  How close is this to the prelab calculation?   ­­­­­___13.8___________

Pull out RL and measured its resistance.  RLmax (experimental)= __1.85Kohm_______.

How close is this to the prelab calculation?   ­­­­­__________1.384kohms____

• □ Calculate the indicated quantities in Table 1, based on the measured values. Fill in Table 1 with these calculations.
• □ Replace the potentiometer with an LED. Observe the brightness. Fill in Table 2 for 1 LED.
• □ Repeat for 2, 3, 4, 5, 6, as many LED’s in series as needed until the brightness diminishes. Fill in the rest of Table 2.

Table 2 – Test of Current Source using Series LED’s as the Load

• □ Pull out the transistor and measure the voltage at the base test point.

VB with transistor removed = ___6.7V_______ ,

Calculate the percent change in VBbetween no transistor and transistor in with RL = 1kW.

% change = _____(6.7-6.56)/6.7*100=________

• □ Insert the 1kW resistor for RLand apply a hot soldering iron to the transistor and observe the collector current.

Does the current increase or decrease when the transistor is heated? ________increase___________.

When you remove the soldering iron, does the current increase or decrease? ________decrease___________.

Post Lab Questions:

1. In step 8, you heated the transistor with a soldering iron and observed the collector current. Recalling from your knowledge of the properties of semi-conductors, what is the effect on conductivity when a semiconductor is heated?

What effect will this have on the transistor currents in a transistor circuit?

2. From the data in Table 1, for what range of load voltage was the transistor in saturation?

For what range of load voltage was the transistor in active operation?

Would you say that the transistor is a more stable current source in active mode or in saturation?

3. Plot a current source regulation curve consisting of measured ICvalues on the y-axis and measured VLvalues on the x-axis. Use Excel or MATLAB.  On the graph, draw a vertical line that separates the active region from the region of saturation.

4. One way to have a stable base voltage is to create a voltage divider such that REQ»(b+1)REis much larger than R2, so that the parallel combination of REQand R2 is approximatelyR  Assuming b = 150, calculate REQ for the circuit used in this lab. Does this result suggest a stable base voltage?

5. Generate an LTspice simulation for R_L= 0W. From the simulation, record all DC currents, and voltages in Table 3.  Paste a screen shot of the simulation below:

6. Repeat step 6 for R_L=R_L(max), as calculated in the Pre-lab. From the simulation, record all DC currents and voltages in Table 3.

7. Repeat step 6 for I_C=9 mA. From the simulation, record all DC currents and voltages in Table 3.

8. Table 1: Compare the load resistor power (at VL= 14 V) with the prelab results.  How close are the two?

9. Table 1: Compare the transistor resistor power (at VL= 0 V) with the prelab results.  How close are the two?

Table 3 –Current Source Simulation in LT Spice

Last Updated on March 4, 2019