I designed a discrete linear voltage regulator to obtain a regulated 5 V DC output from a 9 V supply. The circuit uses a Zener diode as a voltage reference and two NPN transistors connected in a Darlington configuration.
The objective is to maintain the output voltage within ±5% while varying the load resistance. The design will also include current limiting to protect the circuit against excessive load current.
Instead of using a voltage regulator IC, discrete components are used to study voltage regulation, transistor biasing, load regulation, power dissipation and the limitations of the circuit.
The circuit is initially designed and simulated using KiCad/ngspice before hardware implementation.
Design Specifications
| Input voltage | 9 V DC |
| Required output voltage | 5 V DC |
| Output tolerance | ±5% |
| Minimum output voltage | 4.75 V |
| Maximum output voltage | 5.25 V |
| Pass transistor configuration | NPN Darlington pair |
| Voltage reference | Zener diode |
| Simulation software | KiCad/ngspice |
Components Used for Initial Simulation
- 9 V DC voltage source
- 6.8 V Zener diode model
- Two NPN BJT models
- 330 Ω series resistor
- 33 Ω, 47 Ω and 100 Ω load resistors
- KiCad/ngspice
Schematic Diagram
Circuit Description
The circuit consists of a Zener diode reference, a series resistor and two NPN transistors connected in a Darlington configuration.
The Zener diode is reverse-biased and establishes a reference voltage at the base of the first transistor. The resistor limits the current supplied to the reference network.
The two transistors operate in a common-collector (emitter-follower) configuration. Both collectors are connected to the positive supply, the emitter of Q1 is connected to the base of Q2, and the output is taken from the emitter of Q2.
The approximate output voltage is:
Vout = VZ - VBE1 - VBE2
The two base-emitter voltage drops must therefore be considered when selecting the Zener reference.
Selection of the Darlington Configuration
In a single-transistor emitter follower, the base current increases as the load current increases. Since the base is connected to the Zener reference node, this reduces the current available to the Zener.
Applying Kirchhoff's Current Law:
IR = IZ + IB
A significant increase in base current may reduce the Zener current below the level required for accurate voltage regulation.
A Darlington configuration provides a higher effective current gain:
βeff = β1β2 + β1 + β2
For example, assuming each transistor has a current gain of 50:
βeff = 50(50) + 50 + 50 = 2600
At an output current of approximately 100 mA, the input base current of the Darlington pair would be approximately:
IB ≈ 100 mA / 2601 = 38.4 µA
This is considerably smaller than the approximately 1.96 mA required by a single transistor with a current gain of 50 under the same load-current assumption.
The reduced base-current demand helps minimise disturbances to the Zener reference as the load changes. However, the Darlington pair introduces two base-emitter voltage drops and requires additional voltage headroom.
Zener Reference and Series Resistor
The Zener diode provides an approximately constant reference voltage when operated in its reverse-breakdown region with sufficient current.
The resistor current is given by:
IR = (Vin - VZ) / R
An initial 6.2 V reference with a 330 Ω series resistor and 9 V input gives an approximate resistor current of:
IR = (9 - 6.2) / 330 = 8.48 mA
The resistor current divides between the Zener diode and the transistor base.
A lower series resistance increases the current available to the reference network. However, it also increases current consumption and the power dissipated by the resistor and Zener.
The resistor value must therefore be selected by considering the Zener current requirement, the maximum load current, the input-voltage range, and component power ratings.
Selection of Zener Reference Voltage
The initial design used a 6.2 V Zener diode model. Assuming a base-emitter drop of 0.7 V for each transistor:
Vout = 6.2 - 0.7 - 0.7 = 4.8 V
This is within the specified output range of 4.75 V to 5.25 V, but close to the lower limit.
The initial SPICE simulation produced an output voltage of approximately 4.59 V, which was outside the specified tolerance.
The simulated base-emitter voltage drops were approximately 0.773 V for Q1 and 0.893 V for Q2.
Their combined voltage drop was therefore:
VBE(total) = 0.773 + 0.893 = 1.666 V
The reference voltage required for an output of approximately 5 V would be:
Vref = 5 + 1.666 = 6.666 V
A 6.8 V Zener reference was consequently considered because it is a commonly available nominal voltage.
After modifying the breakdown voltage in the SPICE model, the simulated output increased to approximately 5.17 V with a 47 Ω load.
This met the initial ±5% output-voltage requirement.
Load Regulation
Load regulation describes how the output voltage changes as the load current varies.
For a resistive load:
IL = Vout / RL
Reducing the load resistance increases the current drawn from the regulator, provided the circuit can maintain its output voltage.
The regulator was simulated with different load resistances while maintaining a 9 V input.
| Load Resistance | Output Voltage | Load Current (approx.) |
|---|---|---|
| 100 Ω | 5.20 V | 52 mA |
| 47 Ω | 5.17 V | 110 mA |
| 33 Ω | 5.15 V | 156 mA |
As the load resistance decreased from 100 Ω to 33 Ω, the output voltage decreased from 5.20 V to 5.15 V.
The overall change in output voltage was:
ΔVout = 5.20 - 5.15 = 0.05 V
All three operating points remained within the specified output-voltage range.
At the 33 Ω load, the simulated current through the Zener diode was approximately 6.5 mA. This remained above the provisional 5 mA minimum used during the initial design calculations.
Power Dissipation
In a linear regulator, the pass transistor operates with a voltage difference between its collector and emitter while supplying current to the load.
The approximate power dissipation is:
PQ2 ≈ VCE2 × IC2
At the 33 Ω load, the output voltage was approximately 5.15 V and the simulated collector current of Q2 was approximately 155 mA.
The collector-emitter voltage is:
VCE2 = 9 - 5.15 = 3.85 V
Therefore:
PQ2 ≈ 3.85 × 0.155 = 0.597 W
KiCad reported a power dissipation of approximately 595.95 mW for Q2, which was close to the calculated value.
This power is dissipated primarily as heat. The suitability of the transistor therefore depends on its power rating, thermal resistance, maximum junction temperature and safe operating area.
The transistor junction temperature can be estimated using:
TJ = TA + PDRθJA
A suitable pass transistor must be selected before the circuit is physically assembled.
Results
The initial KiCad/ngspice simulations demonstrate that the Zener-referenced Darlington regulator can produce an output within the required 5 V ±5% tolerance under the tested conditions.
The simulated output varied between 5.15 V and 5.20 V for load resistances ranging from 33 Ω to 100 Ω.
The initial 6.2 V Zener reference did not meet the output-voltage specification in simulation. Increasing the nominal breakdown voltage to 6.8 V improved the output voltage.
The simulation also highlighted the importance of considering actual base-emitter voltage drops and transistor power dissipation rather than relying only on ideal approximations.
The present results use generic transistor and Zener SPICE models. They must therefore be verified using models of the selected commercial components and subsequently compared with physical measurements.
Further Development
The next stage involves selecting suitable commercial transistors and a Zener diode, analysing operation over the expected battery-voltage range, and incorporating current-limiting protection.
The regulator will then be assembled and tested to compare experimental measurements with the theoretical calculations and SPICE results.
Transistor Selection
The initial simulations were performed using generic NPN BJT Gummel-Poon models in KiCad/ngspice. These models were sufficient for studying the electrical behaviour of the circuit, but they did not represent the operating limits of specific commercially available transistors.
At a load resistance of 33 Ω, the second transistor (Q2) carried approximately 155 mA collector current and dissipated 595.95 mW.
The transistor selection therefore had to consider the maximum collector current, collector-emitter voltage rating, power dissipation, thermal resistance and maximum junction temperature.
Q2 - BD139 NPN Transistor
The BD139 was selected as a candidate for the main pass transistor because it is a medium-power NPN transistor with higher current and power handling capability than typical small-signal BJTs.
| Parameter | BD139 |
|---|---|
| Maximum collector current | 1.5 A |
| Collector-emitter voltage rating | 80 V (BD139 variant) |
| Power dissipation at 25°C ambient | 1.25 W |
| Junction-to-ambient thermal resistance | 100 °C/W |
| Maximum junction temperature | 150°C |
Using the simulated power dissipation of 0.596 W, the approximate junction temperature at an ambient temperature of 25°C is:
TJ = TA + PDRθJA
TJ = 25 + (0.596 × 100)
TJ ≈ 84.6°C
This estimated temperature is below the maximum junction temperature of 150°C. The BD139 is therefore a reasonable candidate for further evaluation.
However, the transistor must also be checked against its safe operating area, thermal derating characteristics and the expected worst-case operating conditions before hardware implementation.
Datasheet: BD139 - onsemi
Q1 - 2N3904 NPN Transistor
The 2N3904 was selected as a candidate for the first transistor in the Darlington configuration.
Q1 supplies the base current required by Q2 rather than the full load current. Consequently, its current and power requirements are considerably smaller than those of the main pass transistor.
The 2N3904 is a general-purpose, small-signal NPN transistor suitable for investigation in this driver stage.
Its actual base-current requirements, power dissipation and operating conditions will be verified using the selected transistor models.
Voltage Reference - 6.8 V Zener Diode
A nominal 6.8 V Zener diode was selected for the voltage-reference network after the initial 6.2 V model produced an output voltage below the specified range.
The selected physical Zener diode must be evaluated for breakdown-voltage tolerance, test current, dynamic impedance, temperature coefficient and maximum power dissipation.
The nominal voltage alone is not sufficient to guarantee an accurate 5 V output.
Load Resistor Selection
The load resistances of 100 Ω, 47 Ω and 33 Ω were used during simulation to investigate load regulation.
At a 47 Ω load and approximately 5.17 V output, the load resistor dissipates:
PR = Vout2 / R
PR = 5.172 / 47 ≈ 0.569 W
Therefore, a conventional 0.25 W resistor would not be suitable for this operating condition. A 1 W or higher-rated resistor would provide appropriate nominal power capacity, subject to temperature derating and mounting conditions.
For the 33 Ω test, the resistor dissipation is approximately 0.8 W. A higher power rating would be preferable for physical testing.
Power Source Considerations
Although the simulations use an ideal 9 V DC voltage source, the intended initial power source is a rectangular 9 V battery.
The actual battery has internal resistance, limited current-delivery capability and a terminal voltage that decreases during discharge.
The physical prototype may therefore require a lower initial load current or a more capable DC power source.
The final component ratings and operating range will be confirmed before assembly.
No comments:
Post a Comment