# What is Pi Filter : Circuit, Working and Its Applications

The electronic filter is a signal processing filter and these are available in electrical circuit form. The main function of a filter is to allow the DC component of the load of the filter & blocks the AC component of the output of the rectifier. Therefore the filter circuit output will be a stable DC voltage. The designing of a filter circuit can be done using basic electronic components like resistors, capacitors & inductors. The inductor includes a property like it permits only DC signals as well as blocks AC. Similarly, the property of the capacitor is to block the DC signals and supply AC signals. Basically, the electronic filter removes unnecessary frequency components from the signal which we have applied and improves required ones like active/passive, analog/digital, HPF, LPF, BPF, BSF, sampled/continuous-time, linear/non-linear, IIR/FIR, etc. There are some important filters like inductor filter, pi filter, capacitor filter, and LC filter.

## What is Pi Filter?

A Pi filter is one kind of filter which has a two-port, three-terminal block including three elements where each element includes two terminals: The first element is connected across i/p to GND terminal, second terminals are connected across terminals from i/p to o/p and the third element is connected across terminals from o/p to GND. The model of the circuit will be like a ‘Pi’ symbol. The elements used in the circuit are capacitors and one inductor.

### Significance of Pi Filter

The importance of a filter is to attain a ripple-free DC voltage. Basically, filters are efficient while eliminating AC ripples from the rectifier’s o/p voltage. However, the Pi filter is efficient more while eliminating ripples because it includes an additional capacitor on the input area of the circuit.

### Pi Filter Circuit / Design

The pi filter circuit design is shown below. This circuit is designed with two filter capacitors namely C1 and C2 and a choke mentioned with ‘L’. These three components are arranged in the form of greek letter pi. This is the reason that the circuit is named as a pi filter. Here C1 is connected across the o/p of the rectifier; ‘L’ is connected in series & ‘C2’ is connected across the load. Simply one section of the filter is shown however numerous equal sections are frequently utilized to progress the smoothing act.

### Pi Filter Working

The rectifier’s output is applied across the input terminals of the filter like 1 & 2. The filtering act of these three components in the filter circuit is discussed below.

The** first filter capacitor (C1)** provides small reactance toward a.c. component of rectifier o/p output as it gives unlimited reactance toward the d.c. component. So, capacitor C1 avoids a considerable amount of a.c. component whereas the d.c. component maintains its journey toward the choke ‘L’

The **choke (L)** provides approximately zero reactance to the d.c. component and high reactance to the a.c. component. Therefore, it permits the d.c. component to supply through it, whereas the unbiased a.c. component can be blocked.

The **second filter capacitor (C2)** avoids the a.c. the component which the choke has unsuccessful to block. Thus, simply d.c. component shows across the load.

### Characteristics

The** characteristics of the Pi filter** are to produce a high o/p voltage on small current drains. In these filters, the main filtering act can be achieved through the capacitor on C1input. The remaining AC ripples are filtered through a second capacitor and inductor coil.

The high voltage can be attained at the o/p of the filter because the whole input voltage comes into view across the input of the C1 capacitor. The voltage drop across the C2 capacitor & choke coil is pretty small.

Therefore, this is the main benefit of Pi capacitor as it offers high voltage gain. However additionally to the high o/p voltage, the pi filter’s voltage regulation is extremely poor. This is due to the decreased output voltage by the increase in the flow of current throughout the load.

The voltage of the pi filter can be expressed as

**V _{r} = I_{dc}/2fc**

When C =C1 in the pi filter, then the RMS value of o/p voltage can be expressed as

**V _{ac rms}** =

**V**

_{r}/ π√2Substitute the value of ‘Vr’ in the above expression

**V _{ac rms}** =

**V**

_{r}/ π√2 = 1 / π√2 * I_{dc}/2fC1 = I_{dc}Xc1√2Here, **Xc1 = 1/2 ω c1 = 1/4 πfc1**

The above equation is the i/p capacitor’s reactance at 2nd harmonic distortion.

The ripple voltage can be attained by multiplying Xc2/XL

**Now V’ _{ac rms } = V_{ac rms }Xc2/X_{L }**=

**I*** Xc2/X

_{dc}Xc1√2_{L}

The ripple factor formula of the pi filter is

**γ = ****V’ _{ac rms } /Vdc**

** = Idc Xc1 Xc2 √2/V _{dc} X_{L }**

**= Idc Xc1 Xc2 √2/Idc X _{L }= Idc Xc1 Xc2√2/Idc RLX_{L}**

**= Xc1 Xc2 √2/ RLX _{L}**

**γ = ****√2/R _{L} * 1/2 ω c1* 1/2 ω c2* 1/2 ω L**

**= √2/8 ω ^{3} C1 C2LR_{L}**

### Advantages & Disadvantages

The **Advantages of pi filter** include the following.

- The output voltage is high
- Ripple factor is low
- Peak inverse voltage (PIV) is high.

The **disadvantage of pi filter** include the following

- The voltage regulation is poor.
- Large size
- Weighty
- Expensive

### Applications

The **applications of the pi filter** include the following.

- The applications of the pi filter mainly include communication devices to retrieve the exact signal after modulation.
- This filter is mainly used for attenuating noise within signal as well as power lines.
- In communication, the signal can be changed into several high frequencies. Whereas, on the receiver end these filters are applicable for demodulating the exact frequency range.

Thus, this is all about an overview of the pi . Thus, this is all about a pi filter. A filter circuit is used to eliminate the ac components within a rectifier circuit. But this circuit permits the DC components to get to the load. This circuit can be built with passive components like resistors, capacitors, and inductors. The act of filter mainly depends on the electrical properties of components. In the circuit, an inductor blocks DC and allows AC to flow through it whereas the capacitor blocks DC and allows AC. Here is a question for you, what is the other name of the pi filter?