100 Questions on Embedded Hardware and Electronic Technology – Circuit Principles and Applications (Detailed Answers for Beginners)

1. What are the concept, purpose, and methods of frequency compensation in amplifier circuits?

• Concept: By adding RC networks, capacitors, and other components, the frequency characteristics of the amplifier circuit are altered to eliminate self-oscillation and optimize amplification performance.
• Purpose:

1. Stabilize the gain of the amplifier circuit to avoid a sharp drop in gain at high frequencies.
2. Eliminate self-oscillation (caused by a 180° phase shift + gain ≥ 1 at high frequencies), ensuring normal circuit operation.
3. Widen the bandwidth, allowing the circuit to stably amplify signals over a broader frequency range.

• Methods:

1. Lag compensation: Add a small capacitor (e.g., tens of pF) in the high-gain stage of the amplifier circuit to reduce high-frequency gain and disrupt self-oscillation conditions (most commonly used).
2. Lead compensation: Use an RC network to advance the phase of high-frequency signals, offsetting some phase shift to avoid self-oscillation.
3. Miller compensation: Utilize the Miller effect to equivalently amplify the compensation capacitor, reducing its capacitance, suitable for internal compensation of integrated operational amplifiers.

2. What are the common types of filter circuits?

Based on filtering frequency characteristics, there are five common types of filter circuits, which beginners can remember as “function + structure”:

• Low-pass filter (LPF): Allows low-frequency signals to pass while suppressing high-frequency signals (e.g., power supply filtering, removing high-frequency noise).

• High-pass filter (HPF): Allows high-frequency signals to pass while suppressing low-frequency signals (e.g., audio circuits, removing DC interference).

• Band-pass filter (BPF): Only allows signals within a certain frequency range to pass (e.g., radio station selection, sensor signal extraction).

• Band-stop filter (BEF): Suppresses signals within a certain frequency range while allowing other frequencies to pass (e.g., suppressing power frequency interference, removing 50Hz noise).

• All-pass filter: Allows all frequency signals to pass but changes the phase of different frequency signals (e.g., phase correction, signal synchronization).

3. How to identify whether a filter is a low-pass, high-pass, band-pass, or band-stop filter?

Quick identification can be done through “circuit structure” or “frequency response,” with beginners prioritizing structure:

• Low-pass filter: Capacitor in parallel at the output or inductor in series at the input (to block high-frequency signals). Frequency response: The lower the frequency, the greater the output amplitude; after exceeding the cutoff frequency, the amplitude drops sharply.

• High-pass filter: Capacitor in series at the input or inductor in parallel at the output (to block low-frequency signals). Frequency response: The higher the frequency, the greater the output amplitude; below the cutoff frequency, the amplitude drops sharply.

• Band-pass filter: Composed of a low-pass and high-pass filter in series, only allowing intermediate frequency signals to pass. Frequency response: The output amplitude is maximized at a certain intermediate frequency range, dropping outside this range.

• Band-stop filter: Composed of a low-pass and high-pass filter in parallel, suppressing intermediate frequency signals. Frequency response: The output amplitude is minimized at a certain intermediate frequency range, while other frequency signals pass normally.

4. What is the principle of a phase-locked loop (PLL)?

The core of a phase-locked loop (PLL) is “frequency tracking and synchronization,” which beginners can understand as an “automatic frequency modulator.” The principle is divided into three steps:

1. Phase detector (PD): Compares the phase of the input signal (reference signal) with the output signal of the voltage-controlled oscillator (VCO), outputting an error voltage proportional to the phase difference.
2. Low-pass filter (LPF): Filters out high-frequency noise from the error voltage, outputting a stable control voltage.
3. Voltage-controlled oscillator (VCO): Changes the oscillation frequency based on the control voltage, gradually bringing the output signal phase closer to the input signal phase.

• The final result: The VCO output frequency is locked to the input signal frequency, achieving frequency synchronization, and the output frequency can be adjusted through division/multiplication circuits (e.g., multiplied to a higher frequency).

5. How to select a freewheeling diode in a Buck circuit?

In a Buck circuit (step-down circuit), the freewheeling diode provides a loop for the inductor current when the MOSFET is turned off. The selection criteria focus on “fast recovery + low loss”:

• Reverse breakdown voltage (Vr): Must be greater than 1.5-2 times the input voltage (Vin), for example, if Vin=12V, select a diode with Vr≥20V to withstand the inductor’s reverse voltage spikes.

• Maximum forward current (If): Must be greater than the maximum inductor current in the circuit (peak value), for example, if the peak inductor current is 5A, select a diode with If≥8A (to allow for margin).

• Reverse recovery time (trr): Must select a fast recovery diode (trr≤100ns) or Schottky diode to avoid excessive reverse current through the diode when the MOSFET turns on, which increases switching losses (ordinary rectifier diodes have large trr and are unsuitable for high-frequency Buck circuits).

• Forward voltage drop (Vf): Preferably select a Schottky diode with low Vf (around 0.3V) to reduce power loss during freewheeling.

6. Is a larger common-mode rejection ratio (CMRR) better or worse?

A larger common-mode rejection ratio (CMRR) is better.

• Definition: The common-mode rejection ratio is the ratio of differential gain (Ad) to common-mode gain (Ac) (CMRR=20lg|Ad/Ac|), measured in dB, reflecting the ability of the amplifier circuit to suppress common-mode signals (such as interference signals and power supply noise).

• Common understanding: Common-mode signals are identical signals present at both input terminals (e.g., 50Hz power frequency interference), while differential signals are the difference signals between the two input terminals (e.g., useful signals). The larger the CMRR, the stronger the circuit’s ability to suppress common-mode interference, resulting in a purer amplification effect for useful signals.

• Practical application: The CMRR of integrated operational amplifiers is typically above 80dB, and precision amplification circuits (such as sensor signal amplification) require operational amplifiers with CMRR≥100dB.

7. Explain setup time, hold time, and what happens if they are not met?

Setup time and hold time are key timing parameters for flip-flops (such as D flip-flops) in digital circuits, ensuring stable data sampling:

• Setup time (Tsetup): The minimum time that data must remain stable before the clock signal’s triggering edge (e.g., rising edge) arrives. For example, if Tsetup=20ns, the data must be stable and unchanging 20ns before the clock’s rising edge.

• Hold time (Thold): The minimum time that data must continue to remain stable after the clock signal’s triggering edge arrives. For example, if Thold=10ns, the data must remain stable for another 10ns after the clock’s rising edge.

• Consequences of not meeting these requirements: The flip-flop may fail to sample data correctly, leading to “metastability” (an uncertain output state), resulting in logical errors in digital circuits (e.g., microcontrollers collecting incorrect data, communication symbols being lost).

8. What are the consequences of impedance mismatch?

Impedance matching (e.g., transmission line characteristic impedance = load impedance) is critical in high-frequency and communication circuits; mismatches can lead to serious issues:

• Signal reflection: Some signals will reflect back from the load end to the source end, forming standing waves, leading to signal waveform distortion (e.g., square waves turning into sawtooth waves).

• Decreased transmission efficiency: Reflected signals will cancel out some of the incident signals, resulting in reduced power received at the load end (e.g., signal strength attenuation in RF communication).

• Increased electromagnetic interference (EMI): Reflected signals can generate additional high-frequency noise, interfering with surrounding circuits (e.g., clock line reflections causing power supply noise).

• Risk of device damage: Severe reflections can cause voltage spikes that exceed the device’s voltage rating (e.g., impedance mismatch in high-speed buses leading to chip pin breakdown).

9. What are the differences between DCDC and LDO?

DCDC (switching power supply) and LDO (low-dropout linear regulator) are both power regulation devices, with the core differences in “operating principle + performance”:

Comparison Dimension	DCDC	LDO
Operating Principle	Voltage conversion achieved through high-frequency switching of MOSFETs (on/off) combined with inductors and capacitors for energy storage	Stabilizes output voltage by adjusting the voltage drop across a transistor using its linear amplification characteristics
Efficiency	High (80%-95%), especially advantageous when the input-output voltage difference is large	Low (efficiency = output voltage / input voltage ×100%), efficiency decreases as the voltage difference increases

Voltage Difference (Vin-Vout)	Can achieve large voltage differences (e.g., 24V to 5V)	Small voltage difference (usually ≤1V, low-dropout types ≤0.3V), suitable for small range step-down
Ripple	Relatively large (tens to hundreds of mV), requires additional filtering	Very small (a few to tens of μV), output is clean
Size	Large (requires inductors, capacitors, MOSFETs)	Small (only requires input and output capacitors), high integration

Cost	Higher	Lower
Applicable Scenarios	Large voltage differences, high current, battery-powered (requires high efficiency)	Small voltage differences, low current, sensitive to ripple (e.g., analog circuits, chip power supply)

10. Explain the difference between synchronous and asynchronous circuits.

Synchronous and asynchronous circuits are two types of timing structures in digital circuits, with the core difference being “clock control”:

• Synchronous circuits: All flip-flops (logic units) are controlled by the same clock signal, and the circuit’s working rhythm is determined by the clock frequency. For example, the CPU of a microcontroller and the UART communication module operate synchronously under the system clock. Advantages: Clear logic, high stability, easy to design; disadvantages: Clock skew affects high-frequency performance, higher power consumption.

• Asynchronous circuits: There is no unified clock signal; the triggering of flip-flops is directly controlled by changes in input signals (such as levels or edges). For example, asynchronous counters and key debounce circuits can operate without a clock. Advantages: Low power consumption, fast speed (no clock waiting), no clock skew issues; disadvantages: Complex logic, prone to race hazards (signal conflicts), high design difficulty.

11. What is the working principle of linear voltage regulators? What are their advantages and disadvantages compared to switching power supplies?

• Working principle: The core is “linear adjustment tube + feedback control.” The adjustment tube (such as a transistor or MOSFET) operates in the amplification region, detecting output voltage through a sampling resistor, comparing it with a reference voltage to generate an error signal, and adjusting the voltage drop across the adjustment tube to stabilize the output voltage (e.g., keeping the output voltage constant despite fluctuations in input voltage or load changes).
• Advantages:

1. Small output ripple (pure), suitable for circuits sensitive to power supply noise (e.g., analog amplification, precision measurement).
2. Simple circuit structure, low cost, high integration (e.g., LDO chips).
3. No high-frequency switching noise, low electromagnetic interference (EMI).

• Disadvantages:

1. Low efficiency, especially when the input-output voltage difference is large (efficiency = Vout/Vin×100%), with most energy dissipated as heat.
2. Severe heating at large voltage differences, requiring heat sinks, unsuitable for high current or large voltage difference scenarios.
3. Output voltage can only be lower than the input voltage, cannot boost voltage.

12. What is the working principle of a Buck circuit (step-down chopper circuit)? How is the relationship between output voltage and duty cycle derived?

• Working principle: The Buck circuit is a DC step-down circuit, primarily composed of a MOSFET (switch), inductor (L), capacitor (C), and freewheeling diode (D), with the working process divided into two steps:

1. When the MOSFET is on: The input voltage (Vin) is applied across the inductor, storing energy (current increases), while charging the capacitor and supplying power to the load.
2. When the MOSFET is off: The inductor generates a reverse electromotive force (resisting current change), the freewheeling diode conducts, and the inductor releases energy, continuing to charge the capacitor and supply power to the load, maintaining stable output voltage.

• Derivation of output voltage and duty cycle: The duty cycle (D) is the ratio of the MOSFET on time (Ton) to the switching period (T=Ton+Toff) (D=Ton/T). In steady state, the average voltage across the inductor is 0 (volt-second balance), i.e., Vin×Ton = Vout×T. Substituting D=Ton/T gives: Vout = D×Vin (in ideal conditions, neglecting device losses). In practice, due to diode voltage drop, MOSFET on-resistance, etc., Vout is slightly less than D×Vin.

13. What is the working principle of a Boost circuit (step-up chopper circuit)? What are the roles of key components (inductor, capacitor, MOSFET)?

• Working principle: The Boost circuit is a DC step-up circuit, primarily composed of a MOSFET, inductor, capacitor, and diode, achieving voltage boost through energy storage and release in the inductor:

1. When the MOSFET is on: The input voltage is applied across the inductor, storing energy (current increases), while the diode is reverse-biased, and the capacitor discharges to maintain output voltage.
2. When the MOSFET is off: The inductor generates a high reverse electromotive force (adding to the input voltage), the diode becomes forward-biased, and the energy released by the inductor, along with the input voltage, charges the capacitor and supplies power to the load, making the output voltage (Vout) higher than the input voltage (Vin).

• Roles of key components:

1. Inductor (L): The core energy storage component, storing magnetic energy when on and releasing energy to achieve voltage boost when off; the larger the inductance, the more energy stored, and the more stable the output.
2. Capacitor (C): Filters and stores energy, stabilizing output voltage and reducing ripple; the larger the capacitance, the smaller the output ripple.
3. MOSFET: The switching element controlling the charging and discharging time of the inductor; high-frequency switching (e.g., 100kHz-1MHz) can reduce the size of inductors and capacitors.
4. Diode (D): Conducts unidirectionally, preventing the capacitor from discharging back to the input side, while conducting when the MOSFET is off to transfer inductor energy.

14. What is the working principle of a Buck-Boost circuit? In what scenarios requiring wide voltage regulation is it applicable?

• Working principle: The Buck-Boost circuit is a DC conversion circuit that can both step down and step up voltage, primarily composed of a MOSFET, inductor, capacitor, and diode, combining the structures of Buck and Boost circuits:
1. When the MOSFET is on: The input voltage charges the inductor (current increases), the diode is off, and the capacitor discharges to the load.
2. When the MOSFET is off: The inductor generates a reverse electromotive force (opposite to the input voltage), which, when added to the input voltage, charges the capacitor and supplies power to the load through the diode.
3. Output voltage characteristics: When the duty cycle D<0.5, Vout < Vin (step-down mode); when D>0.5, Vout > Vin (step-up mode); in ideal conditions, Vout = [D/(1-D)]×Vin.
• Applicable scenarios:
1. Battery-powered devices (e.g., lithium battery voltage 3.7V-4.2V, requiring output of 3.3V or 5V).
2. Scenarios with large input voltage fluctuations (e.g., solar panel output 12V-24V, requiring stable output of 12V).
3. Devices requiring wide voltage regulation (e.g., powering industrial sensors, needing adjustable 5V-24V).

15. What is the principle of an operational amplifier configured as an inverting proportional amplifier? How is the amplification factor calculated?

• Working principle: In an inverting proportional amplifier circuit, the input signal is connected to the inverting input of the op-amp (-) through a resistor, while the non-inverting input (+) is grounded through a resistor, and the output is fed back to the inverting input through a feedback resistor, utilizing the op-amp’s “virtual short” (V+≈V-) and “virtual open” (input current≈0) characteristics to achieve amplification:
1. Virtual open: The current at the inverting input is approximately 0, so the current through the input resistor (R1) (I1) equals the current through the feedback resistor (Rf) (If).
2. Virtual short: The non-inverting input is grounded (V+=0), so V-≈V+=0 (virtual ground).

• Calculation of amplification factor: I1 = (Vin – V-) / R1 ≈ Vin / R1 (since V-≈0). If = (V- – Vout) / Rf ≈ -Vout / Rf (since V-≈0). From I1=If, we get: Vin/R1 = -Vout/Rf → Voltage amplification factor Av = Vout/Vin = -Rf/R1. The negative sign indicates that the output signal is inverted relative to the input signal, and the magnitude of the amplification factor is determined by the ratio of Rf to R1 (independent of the op-amp’s own parameters).

16. What are the characteristics of input and output impedance in an operational amplifier configured as a non-inverting proportional amplifier?

The input signal is connected to the non-inverting input (+) of the op-amp, and the feedback resistor is connected between the output and the inverting input (-). The core characteristics are “high input impedance, low output impedance”:

• Input impedance: Very high (usually ≥100MΩ), much higher than that of the inverting proportional amplifier. Reason: The input signal is connected to the non-inverting input, where the input current is very small (due to the virtual open characteristic), meaning the circuit has minimal loading effect on the input signal source, making it suitable for scenarios with high source resistance (e.g., sensor output signals).

• Output impedance: Very low (usually ≤100Ω), close to that of an ideal voltage source. Reason: The op-amp’s negative feedback mechanism stabilizes the output voltage, allowing the output to provide a large load current, and the output voltage is less affected by load changes, making it suitable for driving low-impedance loads (e.g., speakers, motor drive circuits).

• Additional: The amplification factor of a non-inverting proportional amplifier is Av=1+Rf/R1 (no inversion), with a gain of at least 1.

17. What is the role of an operational amplifier configured as a voltage follower? In what scenarios requiring isolation or buffering is it applicable?

A voltage follower is a special form of a non-inverting proportional amplifier (Rf=0, R1 open), with an amplification factor Av=1, where the output voltage is identical to the input voltage (in-phase, equal amplitude). The core functions are “buffering, isolation, and impedance conversion”:

• Main functions:
1. Impedance conversion: Converts high input impedance to low output impedance, for example, a sensor with high output impedance (10kΩ) cannot directly drive a low-impedance load (1kΩ); after passing through a voltage follower, the output impedance decreases, allowing stable driving of the load.
2. Signal buffering: Enhances signal driving capability, preventing load changes from affecting the input signal. For example, a microcontroller GPIO output signal can drive more loads after passing through a voltage follower.
3. Isolation: Isolates the input and output sides from each other, for example, isolating analog signals from digital signals through a voltage follower to reduce interference from digital circuits on analog circuits.
• Applicable scenarios:
1. Sensor signal buffering (e.g., thermocouple, pressure sensor output signals).
2. Power supply voltage sampling (e.g., battery voltage connected to ADC through a voltage follower to avoid ADC input impedance affecting sampling accuracy).
3. Isolation between signal sources and loads (e.g., high-frequency signal sources driving low-impedance loads).

18. What is the working principle of a comparator? What are its core differences compared to operational amplifiers (such as response speed, open-loop gain)?

• Working principle: A comparator is a device used to compare the magnitudes of two input voltages, having two input terminals (non-inverting +, inverting -) and one output terminal, with the output having only high (VOH) and low (VOL) states:
1. When the non-inverting input voltage V+ > inverting input voltage V-, the output is high VOH (close to the positive supply voltage).
2. When V+ < V-, the output is low VOL (close to ground or negative voltage).
3. When V+≈V-, the output is in an uncertain state (transition zone).

• Core differences compared to operational amplifiers:

Comparison Dimension	Comparator	Operational Amplifier
Response Speed	Fast (ns level, high-speed comparators ≤10ns)	Slow (μs level, ordinary op-amps ≤1μs)
Open-loop Gain	Lower (usually < 10^5)	Very high (usually ≥10^6)

Operating State	Non-linear operation (no negative feedback, output only high and low levels)	Linear operation (requires negative feedback, output varies continuously)
Output Drive	Strong (can directly drive logic gates, relays)	Weak (requires buffering to drive loads)
Applicable Scenarios	Voltage comparison, threshold judgment, signal shaping	Signal amplification, filtering, operations (addition, subtraction, multiplication, division)

19. What are the working principles of RC integrator and RC differentiator circuits? In what signal processing scenarios are they applicable?

RC integrator and RC differentiator circuits are based on the time-domain characteristics of RC circuits, achieving signal integration or differentiation operations, with the core difference being the “connection method of capacitors and resistors”:

• RC integrator circuit:
1. Structure: The input signal is connected through a resistor R, and the capacitor C is connected in parallel at the output (or RC in series, with output taken from across the capacitor).
2. Working principle: The charging speed of the capacitor is determined by the RC time constant (τ=R×C); when τ is much greater than the input signal period, the output voltage is the integral of the input voltage (Vout≈(1/RC)∫Vin dt).
3. Applicable scenarios: Converting square waves to triangular waves, removing high-frequency noise (low-pass characteristics), timing circuits (e.g., RC delay).
• RC differentiator circuit:
1. Structure: The input signal is connected through a capacitor C, and the resistor R is connected in parallel at the output (or RC in series, with output taken from across the resistor).
2. Working principle: The capacitor charges and discharges quickly; when τ is much smaller than the input signal period, the output voltage is the derivative of the input voltage (Vout≈RC×dVin/dt).
3. Applicable scenarios: Extracting signal edges (e.g., rising and falling edges of square waves), signal shaping (e.g., converting sine waves to sharp pulses), extracting high-frequency signals (high-pass characteristics).

20. What is the function of a differential amplifier circuit? How does it suppress common-mode signals and amplify differential signals?

• Function: Amplifies the difference between two input signals (differential signals) while suppressing the identical parts of both input signals (common-mode signals), mainly used for high-precision signal amplification (e.g., differential output signals from sensors) and interference suppression.
• Principle of suppressing common-mode signals and amplifying differential signals:
1. Differential signal: The difference between the two input signals Vin1 and Vin2 (Vid=Vin1-Vin2), which is the useful signal to be amplified. The amplification factor for differential signals in a differential amplifier circuit is Ad (differential gain), with output Vout=Ad×Vid.
2. Common-mode signal: The identical parts of the two input signals (Vic=(Vin1+Vin2)/2), usually interference signals (e.g., power frequency interference). The amplification factor for common-mode signals in a differential amplifier circuit is Ac (common-mode gain), ideally Ac=0, meaning no common-mode signal in the output.
3. Key: Through symmetrical circuit design (e.g., identical parameters for two transistors, symmetrical resistors), the common-mode signals cancel each other out at the output, while the differential signals are effectively amplified. The common-mode rejection ratio CMRR=Ad/Ac is larger, the stronger the ability to suppress common-mode signals.

21. What are the classifications of power amplifier circuits (Class A, Class B, Class AB, Class C) based on? What are the differences in efficiency and distortion characteristics among the classes?

• Classification basis: Classified based on the conduction angle of the transistor (the angle at which the transistor conducts during one cycle of the input signal).
• Efficiency and distortion characteristics of each class:
1. Class A: Conduction angle = 360° (transistor conducts throughout). Low efficiency (maximum ≤50%), low distortion (output signal is complete), suitable for small signals, low power, and high distortion requirements (e.g., precision instrument amplification).
2. Class B: Conduction angle = 180° (transistor conducts only during half of the input signal cycle). High efficiency (maximum ≤78.5%), but crossover distortion (distortion at the junction of two half-cycle signals) exists, suitable for high power and low distortion requirements (e.g., audio amplifiers).
3. Class AB: Conduction angle between 180°-360° (transistor conducts for more than half of the cycle). Efficiency is relatively high (close to Class B), with small crossover distortion (eliminated through static bias), making it the most commonly used power amplifier type (e.g., audio amplifiers, motor drives).
4. Class C: Conduction angle < 180° (transistor conducts only for a small portion of one cycle of the input signal). Highest efficiency (can reach over 90%), but high distortion (output signal is severely nonlinear), suitable for high-frequency power amplification (e.g., RF communication, radar), requiring resonant circuits to restore signal waveforms.

22. What are the conditions for oscillation in an oscillation circuit (phase balance, amplitude balance)? What are the differences in the applicable frequency ranges between RC sine wave oscillation circuits and LC sine wave oscillation circuits?

• Conditions for oscillation: An oscillation circuit can generate periodic signals without external input signals, requiring two conditions to be met:
1. Phase balance condition: The total phase shift of the circuit is 360° (or 0°), meaning the phase of the feedback signal matches that of the input signal (positive feedback), ensuring the signal is continuously amplified.
2. Amplitude balance condition: The amplitude of the feedback signal is greater than or equal to that of the input signal (loop gain ≥1), ensuring the signal can gradually increase from weak noise to stable oscillation.
• Differences in applicable frequency ranges:
1. RC sine wave oscillation circuit: Frequency is determined by the RC time constant (f=1/(2πRC)). Suitable for low-frequency ranges (a few Hz to several hundred kHz), simple structure, low cost, suitable for generating audio signals and low-frequency signals.
2. LC sine wave oscillation circuit: Frequency is determined by the LC resonant frequency (f=1/(2π√(LC))). Suitable for high-frequency ranges (hundreds of kHz to hundreds of MHz), with high frequency stability, suitable for generating RF signals and high-frequency clock signals.

23. What are the working principles of rectifier circuits (half-wave, full-wave, bridge)? How is the average output voltage calculated?

The function of rectifier circuits is to convert alternating voltage into unidirectional pulsed direct voltage, primarily utilizing the unidirectional conductivity of diodes:

• Half-wave rectification:
1. Working principle: The circuit contains only one rectifying diode; during the positive half-cycle of the AC voltage, the diode conducts, and current flows through the load; during the negative half-cycle, the diode is off, and there is no current through the load, resulting in unidirectional pulsed DC output.
2. Average output voltage (Vavg): Vavg=0.45×V2 (V2 is the effective value of the AC voltage on the secondary side of the transformer).
• Full-wave rectification (center-tapped):
1. Working principle: The transformer secondary has a center tap, and two rectifying diodes are connected in reverse parallel; during the positive half-cycle, one diode conducts, and during the negative half-cycle, the other diode conducts, ensuring unidirectional current through the load, with the output pulsed frequency being twice that of the input.
2. Average output voltage: Vavg=0.9×V2 (V2 is the effective value of the AC voltage on half of the transformer winding).
• Bridge rectification:
1. Working principle: Four rectifying diodes form a bridge; during the positive half-cycle, two diodes conduct, and during the negative half-cycle, the other two diodes conduct, ensuring unidirectional current through the load, with the output pulsed frequency being twice that of the input, without needing a center-tapped transformer.
2. Average output voltage: Vavg=0.9×V2 (V2 is the effective value of the AC voltage on the secondary side of the transformer).

24. In filter circuits, how do capacitor filtering, inductor filtering, and π-type filtering differ in filtering effects and suitable loads (light load / heavy load)?

The function of filter circuits is to reduce the voltage ripple after rectification, making the output DC smoother; different types are suitable for different scenarios:

• Capacitor filtering:
1. Filtering effect: Good filtering effect for high-frequency ripples, small output voltage ripple, simple circuit (only requires parallel capacitors).
2. Suitable load: Light load (high load resistance); under light load, the capacitor discharges slowly, maintaining stable output voltage; under heavy load (low load resistance), the capacitor discharges quickly, resulting in poor filtering effect and large output ripple.
• Inductor filtering:
1. Filtering effect: Good filtering effect for low-frequency ripples, stable output current, strong anti-interference capability.
2. Suitable load: Heavy load (large load current); the inductor resists current changes, stabilizing current under heavy load, resulting in good filtering effect; under light load, the current is small, and the inductor filtering effect is weak, leading to large output voltage ripple.
• π-type filtering (capacitor + inductor + capacitor):
1. Filtering effect: Combines the filtering advantages of capacitors and inductors, providing the best filtering effect and the smoothest output voltage (very small ripple).
2. Suitable load: Suitable for both light and heavy loads, especially for scenarios requiring high ripple performance (e.g., precision instruments, analog circuit power supply), but with a complex structure, higher cost, and larger size.

25. How is the efficiency of a switching power supply calculated? What are the key factors affecting efficiency (such as switching frequency, MOSFET on-resistance, inductor losses)?

• Efficiency calculation: The efficiency (η) of a switching power supply is the ratio of output power (Pout) to input power (Pin), i.e., η=(Pout/Pin)×100%. For example, if the input power is 100W and the output power is 85W, the efficiency is 85%.
• Key factors affecting efficiency:
1. Switching losses: The conduction losses of MOSFETs or transistors (the larger the on-resistance Rdson, the greater the losses) and switching losses (the higher the switching frequency, the greater the switching losses).
2. Inductor losses: Copper losses (losses due to the resistance of the coil DCR) and iron losses (hysteresis and eddy current losses in the iron core, more pronounced at high frequencies).
3. Diode losses: Forward voltage drop (Vf) of the freewheeling diode and reverse recovery losses (the longer the reverse recovery time trr, the greater the losses).
4. Switching frequency: Too low a frequency can lead to larger inductor and capacitor sizes, while too high a frequency increases switching losses and electromagnetic interference, requiring a balanced choice (usually 100kHz-1MHz).
5. Load rate: Switching power supplies are most efficient at 50%-80% load rates; efficiency decreases at light loads (<20%) or heavy loads (>90%).