Section 2.5: Power Supplies & Rectification

Section 2.5: Power Supplies & Rectification

All electronic devices require stable Direct Current (DC) voltage to power internal microchips, logic gates, and analog components. However, utility mains deliver high-voltage Alternating Current (AC). The role of a power supply is to convert this utility AC into clean, regulated DC. This process involves four major stages: transformation, rectification, filtering, and regulation.

Rectification

Rectification is the process of converting bidirectional AC voltage into unidirectional pulsating DC voltage. Diodes, which conduct current in only one direction (from anode to cathode), are the active elements in rectifiers.

Half-Wave Rectifier

A half-wave rectifier uses a single diode in series with the AC source.

• During the positive half-cycle of the AC input, the diode is forward-biased and conducts, allowing current to flow to the load.
• During the negative half-cycle, the diode is reverse-biased and blocks current flow, resulting in zero voltage across the load.

The output of a half-wave rectifier is a series of positive pulses. The average DC output voltage ($V_{DC}$) is:

$$V_{DC} = \frac{V_p}{\pi} \approx 0.318 \cdot V_p$$

where $V_p$ is the peak AC voltage. The frequency of the output ripple is equal to the input AC frequency ($f_{ripple} = f_{in}$). For a standard $60\text{ Hz}$ mains input, the ripple frequency is $60\text{ Hz}$. Because the output is zero for half of the cycle, half-wave rectifiers are highly inefficient (maximum theoretical efficiency of $40.6\%$) and require massive filtering capacitors to smooth the output.

Full-Wave Center-Tapped Rectifier

A full-wave center-tapped rectifier uses two diodes and a specialized transformer with a center-tapped secondary winding. The center tap is connected to ground, acting as the common reference point.

• During the positive half-cycle, the top half of the secondary winding is positive relative to the center tap. Diode 1 is forward-biased and conducts current through the load.
• During the negative half-cycle, the polarity reverses. The bottom half of the winding becomes positive relative to the center tap. Diode 2 is forward-biased and conducts current through the load in the same direction as Diode 1.

The average DC voltage is twice that of a half-wave rectifier:

$$V_{DC} = \frac{2 \cdot V_p}{\pi} \approx 0.636 \cdot V_p$$

where $V_p$ is the peak voltage across one-half of the secondary winding. The ripple frequency is twice the input frequency ($f_{ripple} = 2 \cdot f_{in}$), which is $120\text{ Hz}$ for a $60\text{ Hz}$ input. This higher ripple frequency is much easier to filter. However, each diode must withstand a Peak Inverse Voltage (PIV) of twice the peak secondary voltage ($2 \cdot V_p$).

Full-Wave Bridge Rectifier

A full-wave bridge rectifier uses four diodes arranged in a bridge configuration (Graetz bridge) and does not require a center-tapped transformer.

• During the positive half-cycle, two diagonal diodes (e.g., $D_1$ and $D_2$) conduct, while the other two are reverse-biased.
• During the negative half-cycle, the other two diagonal diodes ($D_3$ and $D_4$) conduct.

In both cycles, current flows through the load in the same direction. The average DC voltage is:

$$V_{DC} = \frac{2 \cdot V_p}{\pi} \approx 0.636 \cdot V_p$$

where $V_p$ is the total peak secondary voltage. The ripple frequency is also $2 \cdot f_{in}$ ($120\text{ Hz}$ for a $60\text{ Hz}$ source). The primary advantages of the bridge rectifier are that it does not require an expensive center-tapped transformer, and the diodes are only subjected to a PIV equal to the peak secondary voltage ($V_p$). The main trade-off is a higher diode voltage drop, as current must pass through two diodes in series, resulting in a $1.4\text{ V}$ drop (for silicon diodes) instead of $0.7\text{ V}$ drop.

Filtering and Ripple Voltage

The output of a rectifier is still a pulsating DC signal that drops to zero volts twice per cycle (in full-wave). To smooth these pulses into a steady DC voltage, a filter capacitor of high value (typically electrolytic) is placed in parallel with the load.

• As the rectified voltage rises to its peak, the capacitor charges rapidly.
• When the rectified voltage begins to fall, the capacitor discharges slowly into the load, maintaining the load voltage.

The small remaining fluctuation in the DC voltage is the ripple voltage ($V_{ripple}$). The peak-to-peak ripple voltage ($V_{ripple(p-p)}$) can be approximated using:

$$V_{ripple(p-p)} = \frac{I_{load}}{f \cdot C}$$

where $I_{load}$ is the load current, $f$ is the ripple frequency, and $C$ is the capacitance of the filter capacitor. Larger capacitors or higher ripple frequencies result in smaller ripple voltages.

Bleeder resistors are always connected in parallel with filter capacitors. These resistors act as a safety feature by providing a discharge path for the capacitor when power is disconnected, preventing dangerous high-voltage shocks to technicians.

Zener Diode Regulation

A capacitor filter alone cannot keep the output voltage constant when the load current or the input AC voltage changes. A regulator is required. The simplest form of voltage regulator is a shunt regulator using a Zener diode.

Zener diodes are designed to operate in their reverse-bias breakdown region. When the reverse voltage across the Zener diode exceeds its rated Zener voltage ($V_Z$), the diode conducts current in reverse while maintaining a nearly constant voltage drop ($V_Z$) across its terminals.

To function as a regulator, a current-limiting series resistor ($R_S$) must be placed before the Zener diode. The series resistor drops the difference between the unregulated input voltage ($V_{in}$) and the regulated output voltage ($V_Z$):

$$R_S = \frac{V_{in} - V_Z}{I_S}$$

where $I_S$ is the sum of the load current ($I_L$) and the Zener current ($I_Z$). If the load current decreases, the Zener diode draws more current to maintain the constant voltage, which wastes power as heat. Zener regulators are therefore limited to low-power, constant-load applications.

Linear vs. Switching Regulators

For higher power applications, electronic circuits use integrated circuit regulators, which fall into two categories: linear and switching.

• Linear Regulators: These regulators operate by using a transistor as a variable series resistor (often called a pass transistor) controlled by a feedback loop. The regulator adjusts the transistor's resistance to maintain a constant output voltage. Excess voltage is dropped across the transistor, which is dissipated as heat. The efficiency ($\eta$) of a linear regulator is approximately:

$$\eta = \frac{V_{out}}{V_{in}}$$

If $V_{in} = 12\text{ V}$ and $V_{out} = 5\text{ V}$, the efficiency is only $41.7\%$, and the remaining $58.3\%$ is lost as heat. Linear regulators (such as the popular 78xx positive and 79xx negative series, e.g., 7805 for $+5\text{ V}$) provide extremely clean, low-noise DC output but require heavy heatsinks.

• Switching Regulators: These regulators operate by rapidly switching a transistor (usually a MOSFET) between fully on (saturated) and fully off (cutoff). When the transistor is on, it conducts current with almost zero voltage drop (low power loss). When it is off, it conducts zero current (zero power loss).

Output voltage is controlled by adjusting the ratio of on-time to off-time, known as the duty cycle, using Pulse-Width Modulation (PWM). Switching regulators use inductors, diodes, and capacitors to store and transfer energy during the switching cycles. They are highly efficient ($85\%\text{--}95\%$) and can step down voltage (Buck regulator), step up voltage (Boost regulator), or invert the polarity. However, they introduce significant high-frequency switching noise into the output, requiring additional filtering, and generate electromagnetic interference.