3.4 DC Power Supplies, Filter Networks, and Voltage Regulators

3.4 DC Power Supplies, Filter Networks, and Voltage Regulators

Key Focus: Modern amateur radio transceivers and station accessories require highly regulated, stable, and transient-free direct current (typically $13.8\text{ V}$ DC at up to $25\text{ A}$ to $30\text{ A}$). Understanding smoothing filters, ripple calculations, linear regulators, Switched-Mode Power Supplies (SMPS), EMI mitigation, and crowbar protection circuits is a major component of the Advanced Theory syllabus.

---

Power Supply Block Architecture

A complete DC power supply transforms raw AC line power ($230\text{ V}_\text{RMS}$ at $50\text{ Hz}$ in Australia) into a stable, isolated DC output through five discrete functional stages:

+-------------+    +-------------+    +-------------+    +-------------+    +-------------+
| 230V Mains  |--->| Transformer |--->|  Rectifier  |--->|  Smoothing  |--->|   Voltage   |---> Regulated
| AC Input    |    | (Step-Down) |    |   Bridge    |    |   Filter    |    |  Regulator  |     DC Output
+-------------+    +-------------+    +-------------+    +-------------+    +-------------+
                                                                                   |
                                                                            +-------------+
                                                                            |  Protection |
                                                                            |  (Crowbar)  |
                                                                            +-------------+

1. Mains Transformer: Steps the AC voltage down (e.g. to $18\text{ V}_\text{RMS}$ for low-voltage transceivers) or up (for valve plate supplies) while providing galvanic isolation between the mains supply and the equipment.
2. Rectifier: Diode network converting bipolar AC into unipolar pulsating DC.
3. Smoothing Filter: Reactive network (capacitors and inductors) attenuating AC ripple variations.
4. Voltage Regulator: Active circuit maintaining constant output voltage despite line voltage swings or load current transients.
5. Protection Circuitry: Electronic failsafes (crowbars, current limiters, thermal shutoffs) preventing transceiver destruction during component failures.

---

Smoothing Filter Networks and Ripple Mechanics

1. Reservoir Capacitor Action

A reservoir capacitor connected across the rectifier output charges to the peak DC voltage ($V_{\text{peak}} = V_{\text{RMS}}\sqrt{2} - 2 V_D$) during the brief interval when the transformer voltage exceeds capacitor voltage. When the rectified input waveform falls below the capacitor voltage, the rectifier diodes turn off, and the capacitor discharges into the load resistance ($R_L$).

• Conduction Angle and Surge Current: The diodes conduct in short charging pulses near each voltage crest; their conduction angle depends on capacitance, load and source impedance. Because the full load charge delivered over the entire half-cycle must be replenished during this short window, the repetitive peak diode current ($I_{\text{peak}}$) is many times larger than the average DC load current ($I_{\text{DC}}$). Diodes must be rated to withstand these intense recurring surge currents.

2. Calculating Peak-to-Peak Ripple Voltage

Assuming approximately linear discharge of the reservoir capacitor between conduction peaks, the peak-to-peak ripple voltage ($V_{\text{ripple(p-p)}}$) is given by:

$$V_{\text{ripple(p-p)}} \approx \frac{I_L}{f_{\text{ripple}} \times C}$$

Rearranging to determine the minimum capacitance required for a specified allowable ripple voltage:

$$C \approx \frac{I_L}{f_{\text{ripple}} \times V_{\text{ripple(p-p)}}}$$

where:

• $I_L$ is the DC load current in Amperes.
• $f_{\text{ripple}}$ is the ripple frequency ($100\text{ Hz}$ for full-wave rectification on $50\text{ Hz}$ Australian mains).
• $C$ is the reservoir capacitance in Farads.
• $V_{\text{ripple(p-p)}}$ is the peak-to-peak ripple voltage in Volts.

---

3. Filter Topologies Compared

CAPACITOR INPUT         CHOKE INPUT             PI FILTER
In+ ----+---+           In+ --[L]--+---+        In+ --+--[L]--+---+
        |   |                      |   |              |       |   |
       [C] [Load]                 [C] [Load]        [C1]    [C2] [Load]
        |   |                      |   |              |       |   |
In- ----+---+           In- -------+---+        In- --+-------+---+

• Capacitor-Input Filter: Delivers high output voltage (approaching $V_{\text{peak}}$ at light loads), but exhibits poorer voltage regulation (output drops significantly under heavy current) and severe peak diode current pulses.
• Choke-Input Filter (L-C Filter): The inductor is placed in series between the rectifier and the capacitor. The inductor opposes sudden changes in current, maintaining continuous current conduction through the diodes over the entire cycle. The DC output voltage equals the average value of the rectified waveform:

$$V_{\text{DC}} \approx \frac{2 V_{\text{peak}}}{\pi} \approx 0.636 \times V_{\text{peak}} \approx 0.90 \times V_{\text{RMS}}$$

Choke-input filters provide superior voltage regulation under varying load conditions and low peak diode stress. To prevent the filter from behaving as a capacitor-input filter at light loads, the inductor must exceed the critical inductance ($L_c$):

$$L_c \ge \frac{R_{L(\text{max})}}{3 \omega} = \frac{R_{L(\text{max})}}{6 \pi f_{\text{line}}} \approx \frac{R_{L(\text{max})}}{942}\text{ Henrys (at } 50\text{ Hz mains)}$$

• $\pi$-Section (CLC) Filter: Comprises a capacitor-input stage followed by a series choke (or resistor) and a second shunt capacitor. Provides exceptional ripple attenuation ($40\text{ dB}$ to $60\text{ dB}$ reduction), making it ideal for low-current audio preamplifiers and receiver local oscillator supplies.
• Bleeder Resistors: Connected across the output of filter capacitor banks to discharge stored energy safely upon power-down, and to maintain the minimum critical load current ($I_{\text{critical}}$) in choke-input filters to prevent voltage soaring at no-load.

---

Linear Voltage Regulators

Linear power supplies utilize an active semiconductor pass element operating in its active/linear region, functioning as a dynamically controlled variable resistor in series with the load.

Unregulated Vin ---> C [ NPN pass transistor ] E ---> [R_E] ->+---> Vout / Load
                                  B                           |
                                  ^                          [R1]
                                  |                           |
                        [Error amplifier] <------ V_fb -------+
                         (+) V_ref  (-) V_fb                  [R2]
                                                              |
                                                             GND

The error amplifier drives the base. $R_E$ is an optional series emitter ballast resistor; $R_1$ and $R_2$ sense the output after it. The load returns to the common ground.

Series-Pass Transistor Architecture

1. Reference Element: A precision Zener diode or bandgap voltage reference establishes an ultra-stable voltage ($V_{\text{ref}}$).
2. Sampling Network: A resistive voltage divider ($R_1, R_2$) samples a fraction of the output voltage: $V_{\text{fb}} = V_{\text{out}} \times R_2 / (R_1 + R_2)$.
3. Error Amplifier: A high-gain differential op-amp compares $V_{\text{fb}}$ with $V_{\text{ref}}$.
4. Negative Feedback Correction: If $V_{\text{out}}$ drops due to an increased transceiver current demand, $V_{\text{fb}}$ decreases. The error amplifier detects this discrepancy and increases base drive current to the series-pass transistor. The pass transistor conducts more heavily, reducing its collector-to-emitter voltage drop ($V_{CE}$) and restoring $V_{\text{out}}$ to its precise regulated setpoint.

Three-Terminal Integrated Circuit Regulators

• Fixed Regulators (78xx / 79xx Series): Three-terminal ICs delivering fixed positive (7805 $= +5\text{ V}$, 7812 $= +12\text{ V}$, 7815 $= +15\text{ V}$) or negative (79xx) rails with built-in thermal overload and short-circuit protection.
• Adjustable Regulators (LM317): Develops a precise $1.25\text{ V}$ reference voltage ($V_{\text{ref}}$) between its output and adjustment terminals:

$$V_{\text{out}} = 1.25\text{ V} \left( 1 + \frac{R_2}{R_1} \right) + I_{\text{adj}} R_2$$

$I_{\text{adj}}$ is typically $50\ \mu\text{A}$, with a $100\ \mu\text{A}$ maximum. Its $I_{\text{adj}}R_2$ contribution is often small, but include it when calculating output accuracy.

• Dropout Voltage: The minimum input-to-output differential voltage ($V_{\text{in}} - V_{\text{out}}$) required across the regulator to maintain stable regulation. For standard linear ICs, dropout is $2.0\text{ V}$ to $2.5\text{ V}$. Low-Dropout (LDO) regulators utilize P-channel MOSFETs or PNP pass transistors to achieve dropout voltages below $0.2\text{ V}$ to $0.4\text{ V}$.

Power Dissipation and Thermal Constraints

The fundamental drawback of linear regulators is low efficiency under high current or large voltage differentials. The series-pass device absorbs the full difference between input and output voltage:

$$P_D = (V_{\text{in}} - V_{\text{out}}) \times I_L$$ $$\text{Efficiency } (\eta) \approx \frac{V_{\text{out}}}{V_{\text{in}}} \times 100\%$$

For a $13.8\text{ V}$, $20\text{ A}$ linear power supply supplied by an unregulated $20\text{ V}$ DC rail, the pass transistors must dissipate:

$$P_D = (20\text{ V} - 13.8\text{ V}) \times 20\text{ A} = 6.2\text{ V} \times 20\text{ A} = 124\text{ Watts}$$

This $124\text{ W}$ of continuous waste heat demands massive extruded aluminum heatsinks, thermostatically controlled cooling fans, and multiple paralleled pass transistors (such as three or four 2N3055 power BJTs) fitted with low-value emitter ballast resistors ($0.1\ \Omega$) to ensure equal current sharing and prevent current hogging.

---

Switched-Mode Power Supplies (SMPS)

Switched-Mode Power Supplies can achieve efficiencies of $85\%$ to $95\%$ by rapidly switching between off and a low-loss on-state. A fully enhanced power MOSFET uses its ohmic region; an IGBT has a low on-state collector-emitter drop. Real devices dissipate conduction and switching-transition losses.

+-------------+    +-------------+    +-------------+    +-------------+    +-------------+
| 230V Mains  |--->| Mains Bridge|--->| High-Voltage|--->| High-Freq   |--->| Fast        |---> Regulated
| AC Input    |    | Rectifier   |    | Inverter    |    | Ferrite     |    | Schottky    |     13.8V DC
+-------------+    +-------------+    | (PWM Switch)|    | Transformer |    | & LC Filter |     Output
                                      +-------------+    +-------------+    +-------------+
                                             ^                                     |
                                             |          PWM Feedback Loop          |
                                             +-------------------------------------+

Principles of Operation

1. Direct Mains Rectification: The incoming $230\text{ V}$ AC mains is rectified directly by a bridge rectifier and smoothed, producing a high-voltage DC bus of approximately $325\text{ V}$ DC ($230\text{ V} \times \sqrt{2}$).
2. High-Frequency Inverter: High-voltage power MOSFETs chop this $325\text{ V}$ DC bus into high-frequency pulses at switching frequencies from $50\text{ kHz}$ to $1\text{ MHz}$.
3. Compact Ferrite Transformer: Higher frequency reduces the volt-seconds applied during each switching interval, allowing fewer turns or a smaller core cross-section for a given flux swing. At $100\text{ kHz}$ the frequency is 2,000 times $50\text{ Hz}$, enabling much smaller magnetics. Core losses, winding current, insulation and cooling also determine size; core volume is not simply proportional to $1/f$.
4. Secondary Rectification and Filtering: The stepped-down high-frequency AC is rectified with fast Schottky diodes and smoothed by small inductors and low-ESR capacitors.
5. Pulse-Width Modulation (PWM) Regulation: Feedback regulates the output by adjusting switching duty cycle ($D=t_{\text{on}}/T$). For an ideal forward converter in continuous-conduction mode, the relationship is:

$$V_{\text{out}} = D \times \frac{N_s}{N_p} \times V_{\text{bus}}$$

SMPS Topologies

The following buck and boost equations assume ideal components and continuous inductor current; other topologies and discontinuous operation use different relationships.

• Buck Converter: Non-isolated step-down converter ($V_{\text{out}} = D \times V_{\text{in}}$).
• Boost Converter: Non-isolated step-up converter ($V_{\text{out}} = V_{\text{in}} / (1 - D)$).
• Half-Bridge / Full-Bridge Converters: Transformer-isolated topologies used in standard high-current amateur station supplies.

RFI Disadvantages and Amateur Station Mitigations

Because SMPS units switch high voltages and currents with extremely fast rise and fall times ($di/dt$ and $dv/dt$), they generate intense broadband electromagnetic interference (EMI) and RF switching "hash" spanning $100\text{ kHz}$ to $100\text{ MHz}$:

• Conducted and Radiated EMI: Harmonics radiate through the air or conduct out through mains leads and DC power cables.
• Mitigations:
  1. Line Filters: Installing common-mode line filters containing bifilar toroidal chokes and Class-X and Class-Y safety capacitors on both AC mains and DC output rails.
  2. Chassis Shielding: Enclosing the power supply in a fully shielded, grounded steel or heavy aluminum enclosure.
  3. Ferrite Suppressors: Clamping snap-on type 31 or 43 ferrite cores over external DC supply cables.
  4. The "Noise Offset" Knob: Specialized amateur radio SMPS units feature a front-panel "Noise Offset" (or frequency shift) control. Turning this potentiometer adjusts the internal oscillator switching frequency slightly (e.g. from $65\text{ kHz}$ to $68\text{ kHz}$). This shifts the high-order harmonics and receiver "birdies" away from the active receive frequency, moving interference completely out of the receiver passband.

---

Power Supply Comparison

---

Power Supply Protection Mechanisms

Supply + ----[DC fuse]----+----------------------> Load +
                         |
                         A
                       [SCR] <--- Gate drive from over-voltage sensor
                         K
                         |
Return ------------------+----------------------> Load -

The sensor monitors the protected output relative to return. The SCR is connected across that output, downstream of the fuse; no wire bypasses the fuse.

1. Over-Voltage Crowbar Circuit

Many amateur transceivers use a nominal $13.8\text{ V}$ supply; use the particular equipment's permitted voltage range. If a series-pass transistor fails collector-to-emitter short, the unregulated input can reach the output and damage the load.

An over-voltage crowbar responds as follows:

1. A Zener/reference sensing circuit monitors the output. Select its threshold and tolerances below the load's damaging voltage while allowing normal supply variation.
2. An over-voltage triggers a high-current SCR connected across the protected output.
3. The conducting SCR pulls the output down toward its low on-state voltage and diverts fault current from the load.
4. Coordinated current limiting, a fuse, a breaker or shutdown circuitry then controls or disconnects the fault. Fuse clearing takes time: the SCR must withstand capacitor-discharge and source current, and the complete protection response must meet the load's voltage/time tolerance.

2. Current Limiting Strategies

• Constant Current Limiting: If the load current reaches a preset threshold ($I_{\text{limit}}$), the regulator clamps the current to that value while allowing output voltage to drop. However, if a dead short occurs ($V_{\text{out}} = 0\text{ V}$), the entire unregulated input voltage appears across the series-pass transistor while conducting $I_{\text{limit}}$. The transistor dissipates maximum power ($P_D = V_{\text{in}} \times I_{\text{limit}}$), leading to thermal destruction unless heavily over-heatsinked.
• Foldback Current Limiting: Senses both output current and output voltage. When an overload occurs, the circuit reduces (folds back) both voltage and current simultaneously. Under a dead short, the output current drops to a small fraction of rated maximum ($I_{\text{short}} \ll I_{\text{limit}}$, typically $10\%$ to $20\%$ of full load). This drastically curtails transistor power dissipation during fault conditions, allowing safe, sustained short-circuit survival.
• Reverse Polarity Protection: A diode connected across the protected input, normally reverse-biased, conducts if polarity is reversed. It limits reverse voltage while a coordinated upstream fuse clears or the source current limit operates. The diode must withstand the fault current until protection acts.

---

Worked Engineering Calculations

Example 1: Smoothing Capacitor Sizing for an Amateur Power Supply

Problem: An amateur builds a $13.8\text{ V}$ linear power supply designed to deliver a continuous load current of $I_L = 20\text{ A}$ to an HF transceiver. The supply uses a full-wave bridge rectifier fed by a $50\text{ Hz}$ Australian mains transformer. Calculate:

1. The fundamental ripple frequency ($f_{\text{ripple}}$).
2. The minimum filter capacitance ($C$) required to keep the peak-to-peak ripple voltage below $V_{\text{ripple(p-p)}} = 1.5\text{ V}$.

Solution:

1. Ripple Frequency: Full-wave bridge rectification rectifies both halves of the $50\text{ Hz}$ line:

$$f_{\text{ripple}} = 2 \times f_{\text{line}} = 2 \times 50\text{ Hz} = 100\text{ Hz}$$

1. Capacitance Calculation:

$$C = \frac{I_L}{f_{\text{ripple}} \times V_{\text{ripple(p-p)}}} = \frac{20\text{ A}}{100\text{ Hz} \times 1.5\text{ V}} = \frac{20}{150} = 0.1333\text{ Farads}$$ $$C = 133,333\ \mu\text{F}$$

(Three $47,000\ \mu\text{F}$ capacitors in parallel provide a nominal $141,000\ \mu\text{F}$. Practical selection must also allow for capacitance tolerance, ripple-current and voltage ratings.)

---

Example 2: Linear Regulator Thermal Dissipation and Heatsink Requirements

Problem: A $13.8\text{ V}$ linear power supply draws an unregulated $19.5\text{ V}$ DC at its filter capacitor output while delivering $I_L = 15\text{ A}$ continuous to a VHF FM repeater transmitter.

1. Calculate the power dissipated as heat in the series-pass transistor bank.
2. Calculate the electrical efficiency ($\eta$) of the power supply stage.
3. If four 2N3055 transistors share the current equally, calculate the power dissipated per transistor.

Solution:

1. Total Thermal Dissipation:

$$P_D = (V_{\text{in}} - V_{\text{out}}) \times I_L = (19.5\text{ V} - 13.8\text{ V}) \times 15\text{ A} = 5.7\text{ V} \times 15\text{ A} = 85.5\text{ Watts}$$

1. Power Supply Stage Efficiency:

$$P_{\text{out}} = V_{\text{out}} \times I_L = 13.8\text{ V} \times 15\text{ A} = 207.0\text{ Watts}$$ $$P_{\text{in}} = V_{\text{in}} \times I_L = 19.5\text{ V} \times 15\text{ A} = 292.5\text{ Watts}$$ $$\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\% = \frac{207.0\text{ W}}{292.5\text{ W}} \times 100\% = 70.77\%$$

1. Dissipation per Transistor: Across four paralleled transistors:

$$P_{D(\text{each})} = \frac{85.5\text{ W}}{4} = 21.38\text{ Watts per transistor}$$

(Each transistor requires low-value emitter ballast resistors, such as $0.1\ \Omega$, and an appropriately rated heatsink to maintain junction temperatures well below the $200^\circ\text{C}$ maximum rating).