Analog & Circuit Analysis

In the real world, signals are analog—continuous voltages and currents that represent physical phenomena. Understanding how to process, convert, and analyze these signals is essential for bridging the gap between the digital microcontroller and the physical world.

[Diagram: Analog signal → ADC → Digital Processing → DAC → Analog output]

Operational Amplifiers (Op-Amps)

Op-Amps are the building blocks of analog circuits. They can amplify, filter, and condition signals before they reach your microcontroller.

Key Op-Amp Configurations

Inverting Amplifier: Output is inverted and amplified. Gain = -Rf/Rin
Non-Inverting Amplifier: Output is in-phase with input. Gain = 1 + Rf/Rin
Voltage Follower (Buffer): Unity gain, high input impedance. Used for impedance matching.
Summing Amplifier: Adds multiple input signals together.
Differential Amplifier: Amplifies the difference between two inputs.

💡 Pro Tip: Always check the op-amp's slew rate and bandwidth (GBW) to ensure it can handle your signal frequency!

Analog-to-Digital Conversion (ADC)

ADCs convert continuous analog voltages into discrete digital values that your microcontroller can process.

Key ADC Parameters

Resolution: Number of bits (e.g., 10-bit = 1024 levels, 12-bit = 4096 levels)
Sampling Rate: How fast the ADC can take samples (Samples per second)
Reference Voltage (Vref): The voltage that corresponds to the maximum digital value
Quantization Error: Inherent error due to discrete levels = Vref / (2^n)

Digital Value = (Vin / Vref) × (2^n - 1)

ADC Types

Successive Approximation (SAR): Good balance of speed and resolution. Most common in MCUs.
Flash ADC: Very fast, but expensive and power-hungry.
Delta-Sigma (ΔΣ): High resolution, slower. Great for precision measurements.

Digital-to-Analog Conversion (DAC)

DACs do the opposite—they convert digital values back to analog voltages for driving speakers, motors, or generating waveforms.

Vout = (Digital Value / (2^n - 1)) × Vref

Common DAC Architectures

R-2R Ladder: Simple resistor network, commonly used
Weighted Resistor: Different resistor values for each bit
PWM-based DAC: Using PWM with low-pass filter to approximate analog output

Pulse Width Modulation (PWM)

PWM is a technique to encode analog-like values using digital signals by varying the duty cycle.

[Diagram: PWM waveforms at 25%, 50%, and 75% duty cycles]

PWM Applications

Motor Speed Control: Vary duty cycle to control average voltage
LED Dimming: Control brightness without changing voltage
Audio Generation: Create tones and simple waveforms
Power Supply Regulation: Switch-mode power supplies

Average Voltage = Duty Cycle × Vmax

Signal Conditioning

Before feeding analog signals to an ADC, they often need conditioning:

Common Conditioning Techniques

Amplification: Boost weak signals to ADC input range
Filtering: Remove noise and unwanted frequencies (Low-pass, High-pass, Band-pass)
Level Shifting: Shift bipolar signals to unipolar range
Clamping/Protection: Prevent overvoltage damage to ADC inputs

Practical Example: Temperature Sensor Interface

Reading an analog temperature sensor (like LM35) involves:

          // LM35 outputs 10mV per °C // With 3.3V reference and 10-bit ADC:
          uint16_t adc_value = read_adc(TEMP_CHANNEL); float voltage =
          (adc_value / 1023.0) * 3.3; float temperature_c = voltage * 100; //
          10mV/°C = 100°C/V
        

🎯 Key Takeaway: Understanding analog electronics allows you to interface with the physical world—sensors, actuators, and audio—effectively bridging the analog-digital divide.