# Equations and Calculator: Bidirectional Buck and Boost DC-DC Converter

#### 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:

Vout​ = 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:

Vout ​=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