Pulse Width Modulation (PWM) is a versatile technique used in electronics for controlling power to devices, including LEDs and motors. While effective for many applications, the inherently pulsating nature of PWM can introduce flicker in lighting applications or instability in voltage-sensitive circuits. To mitigate this, signal smoothing through an RC (Resistor-Capacitor) filter can transform a PWM signal into a more stable, continuous voltage suitable for various applications, including setting thresholds in comparators.

**Objective**

This experiment aims to demonstrate the smoothing of a PWM signal using an RC filter. By adjusting the PWM frequency and observing the effect of the RC filter, we aim to explore the relationship between PWM frequency, filter characteristics, and signal smoothing effectiveness.

**Materials and Setup**

- Red Pitaya or equivalent function generator and oscilloscope
- Resistor: 10 kOhm
- Capacitor: 1 ÂµF
- Optional: Voltage buffer (OpAmp follower) for connecting the filtered signal to loads other than high impedance

**Circuit Assembly**

**RC Filter Connection:**Configure the RC filter by connecting the 10 kOhm resistor in series with the 1 ÂµF capacitor across the output of the PWM signal generator. The combination forms an RC filter with a specific time constant.**Circuit Schematic for Clarity:**

**Conducting the Experiment**

**PWM Frequency Variation:**Generate a PWM signal at varying frequencies (100 Hz, 1 kHz, and 10 kHz) and observe the effect of the RC filter on the signal's smoothing at each frequency.**At 100 Hz PWM:****At 1 kHz PWM:****At 10 kHz PWM:**

**Analysis and Observations**

**Signal Smoothing Efficiency:**The effectiveness of the RC filter in smoothing the PWM signal increases with the PWM frequency. At higher frequencies (e.g., 10 kHz), the output signal appears significantly smoother compared to lower frequencies.**Time Constant and Filter Design:**The time constant of the RC filter (*Ï„*=*R*Ã—*C*) is critical in determining its smoothing capability. With a 10 kOhm resistor and a 1 ÂµF capacitor, the filter's time constant dictates its cutoff frequency and, consequently, its ability to smooth the PWM signal effectively.

**Relevant Equation**

The time constant (*Ï„*) of an RC filter, which significantly impacts its smoothing ability, is calculated as:

where:

*Ï„*is the time constant in seconds,*R*is the resistance in ohms,*C*is the capacitance in farads.

The cutoff frequency (*fc*) of the RC filter, determining its responsiveness to signal changes, is given by:

**Conclusion**

This experiment illustrates the practical application of an RC filter in smoothing a PWM signal, highlighting the importance of selecting appropriate component values to achieve desired signal characteristics. By adjusting the PWM frequency and employing an RC filter, we can transform a pulsating PWM signal into a stable, continuous voltage, suitable for applications requiring steady voltage inputs. However, the limitations in response time imposed by the filter's time constant also underline the importance of careful design consideration, especially when rapid signal changes are necessary. This foundational understanding paves the way for further exploration into advanced signal conditioning and filtering techniques in electronic design.