# Low Pass Filter

We have figured out that we’ll be using a Peltier Element which forms the major component of this project, and we are aware that controlling the magnitude of current through Peltier would help us control its temperature.
The question is how do we control the magnitude of current which is very high (upto 4 Amperes) relative to the current that Arduino pins provide which is only in milli-Amperes

The first thing that strikes at such a problem is PWM!
However the problem with PWM pulses is that they are abrupt, they go ON and OFF.Such abrupt changes destroy peltier. Peltier requires smooth current which can be obtained through an LPF.

A Stack Exchange answer helped us out giving us the schematic of a filter that takes PWM pulses from Arduino as inputs and produces Output current Magnitude depending on the pulse width.

##  Explanation of Filter Values and Calculations:

The circuit uses a low pass LC filter with the inductor connected to the ground line via transistor switches. The diodes act as flyback diodes. The 2 transistors can be operated either using the same pwm signal or using 2 pwm signals that are 180° out of phase.

If 2 pwm signals are used, then the effective frequency filtered by the filter is twice of that of the pwm signals. This results in greater attenuation and smoothening of the current to the peltier. However, many microcontrollers don’t have the ability to provide out of phase pwm signals.

For a single pwm signal driving both the transistors, the advantage of higher frequency being filtered is lost but it can be implemented by most of the microcontrollers available in the market.

For a low pass LC filter,
f = 1 / (2π sqrt(LC))

Substituting the values, the cutoff frequency comes out to be 734 Hz. The Arduino can provide a maximum frequency of 25 KHz which is way above the cut off frequency which ensures sufficient smoothing for the peltier. Higher harmonic frequencies are attenuated further. The particular values of L and C were selected as they suffice the needs of the filter and are readily available.

The voltage rating of the capacitor should be higher than the peltier maximum voltage. Therefore,a rating above 15V should be enough.

The advantage of 2 inductor branches is that the maximum current rating required for each inductor is reduced. Higher current rating inductors are more expensive. Since the maximum peltier current of 6 A is shared by 2 branches, the current flowing through each branch would max out at 3 A. Hence, an inductor of ~3.5 A would be sufficient.

## Testing the Filter Circuit in LTSPice

We tested this schematic in LTSpice and following are the simulation results for LTSpice Simulation of the Low Pass Filter circuit. The 3 Ohm Resistor represents the Peltier Element.

When PWM duty cycle is zero, no current flows through the resistor. For PWM Duty Cycle 25%