**Bidirectional Buck and Boost Converter**

Below is the Circuit Diagram, Equations and Calculator for Calculating different aspects like Power, Current and Voltage average, Inductance, Switch On and off time etc in a Bidirectional Buck and Boost DC to DC converter. I will write an article separately explaining the workings of DC to DC converter.

Assuming Duty Cycle Ds1 and Voltage Source Vin = VHVbus, Vout = Vbattery is constant. V12average = DS1*VHVbus.

Then

No Power Flow Vout (battery) = V12 average

Buck Operation Vout (battery) < V12 average

Boost Operation Vout (battery) > V12 average

**Equations**:

Ds1 = Ton/Toff

T = Ton + Toff

Ds2 = ( 1 – Ds1)

T = 1 / f

V12 = Ds1 * VHVbus

I av = (V12 – Vbatt) / R

P0 = I av * Vbatt

VL (on) = VHVbus -Vbatt-Iav*R

ΔI = ( VL (on) * Ton ) / L

VL (off) = ( – Vbatt) – (I av * R)

ΔI = ( VL (off) * Toff ) / L

**Where**

Vout is the output Voltage

V12 is the average voltage across Switch 2

Vin is the input voltage

Ds1 is the duty cycle of the Switch S1

Ds2 is the duty cycle of the Switch S2

f is the switching frequency of the semiconductor Switch

T is the time period of the semiconductor Switch

Ton is the ON time of the semiconductor Switch

Toff is the OFF time of the semiconductor Switch

I av is the average current through the Inductor the sign of I av determines the direction of Power Flow

R is the Resistance of the Inductor

P0 is the power Delivered to the output Voltage V out

Interactive animation from TU Delft University

Below is Individual Buck Converter and Boost Converter Circuit Diagram and equations. Calculator to be added later for this one.

**Buck Converter:**

*V*out = *DVin*

*T* = *1/f*

*D* = *Ton* / (*T* )

*T = Ton + Toff*

Where

Vout is the output Voltage

D is the duty cycle of the Switch

Vin is the input voltage

f is the switching frequency of the semiconductor Switch

T is the time period of the semiconductor Switch

Ton is the ON time of the semiconductor Switch

Toff is the OFF time of the semiconductor Switch

**Boost Converter**:

*V*out =*Vin* / ( 1 – *D* )

*T* = *1/f*

*D* = *Ton* / (*T* )

*T = Ton + Toff*

Where

Vout is the output Voltage

D is the duty cycle of the Switch

Vin is the input voltage

f is the switching frequency of the semiconductor Switch

T is the time period of the semiconductor Switch

Ton is the ON time of the semiconductor Switch

Toff is the OFF time of the semiconductor Switch