The SCRs or Silicon Controlled Rectifiers are four-layer semiconductor devices intended to be used as power controls and relaxation oscillators. The symbol and characteristic of this component is showin in figure. As the SCR operates triggered by external devices in a on/off mode there are few quantities to be calculated when using them in practical projects.

**Formula 1**

Trigger current:

I_{T} = Ico / ( 1 – a1 + a2 )

**Where: **

I_{T} is the trigger current in amperes (A)

Ico is the leakage current in amperes (A)

a1 is the gain of first transistor

a2 is the gain of second transistor

Note: the parameter I_{T} usually is given by the SCR's manufacturer and is in the range between 0.1 mA and 100 mA to common types.

**Formula 2 **

Power per cycle:

Pd = (Va x Ia x tr ) / 4.6

**Where: **

Pd is the power dissipation oper cycle in watts (W)

Va is the anode voltage prior to switching in volts (V)

Ia is the anode current after switching in amperes (A)

tr is the switching time for anode-cathode voltage to fall from 90% to 10%

**Formula 3 **

Average Power:

Pd = (f x Va X Ia X tr) / 4.6

**Where: **

Pd is the average power dissipation in watts (W)

f is the switching frequency in hertz (Hz)

Va is the anode voltage prior to switching in volts (V)

Ia is the anode current after switching in amperes (A)

**Formula 4 **

DC application:

Pd = Vs x Id

**Where: **

Pd is the dissipated power in watts (W)

Vs is the voltage fall with the SCR in the on-state also called saturation voltage in volts (V)

Id is the forward current in amperes (A)

Note: to common SCRs the typical value for Vf is 2.0 V.

**Formula 5 **

Load voltage vs Trigger Delay (angle α) - half wave application

UL = (Up / 2 x π) x (1 + cos α)

**Where: **

UL is the voltage in the load (instantaneous) in volts (V)

Up is the peak voltage of the sine input voltage in volts (V)

π is 3.1416

cos α is the cosine of the conduction angle in degrees

**Derivated formulas:**

**Formula 6**

Load voltage for full wave application :

UL = (Up / π) x (1 + cos α)

**Where: **

UL is the instantaneous value of the load voltage in volts (V)

Up is the peak value of the sine wave input voltage in volts (V)

π is 3.1416

cos α is the cosine of the conduction angle in degrees

**Application example: **

A SCR is used to control a DC load in a 5 A circuit. What is the power dissipated by this device? Given the saturation voltage = 2.0 V.

**Data: **

Us = 2.0 V

Id = 5 A

Pd = ?

**Using formula 4:**

Pd = 2.0 x 5 = 10 W