5.1.1 Power Dissipation Calculations

The internal power dissipation within the MCP1781 is a function of input voltage, output voltage, output current and quiescent current. Equation 5-1 can be used to calculate the internal power dissipation for the LDO.

$P_{LDO}=\left(V_{IN\left(MAX\right)}-V_{OUT\left(MAX\right)}\right)\times I_{OUT\left(MAX\right)}$

Where:

P_LDO = Internal power dissipation of the LDO pass device

V_IN(MAX) = Maximum input voltage in the application

V_OUT(MIN) = LDO minimum output voltage

I_OUT(MAX) = Maximum output current in the application

In addition to the LDO pass element power dissipation, there is power dissipation within the MCP1781 because of quiescent or ground current. The power dissipation as a result of ground current can be calculated by applying Equation 5-2:

$P_{I\left(GND\right)}=V_{IN\left(MAX\right)}\times I_{GND}$

Where:

P_I(GND) = Power dissipation due to the ground current of the LDO

V_IN(MAX) = Maximum input voltage in the application

I_GND = Current flowing into the GND pin

The total power dissipated within the MCP1781 is the sum of the power dissipated in the LDO pass device and the ground current power dissipation term. Because of the CMOS construction, the I_GND for the MCP1781 is typically 85µA at full load. Operating at a maximum V_IN of 55V results in a power dissipation of 4.675 mW. For most applications, this is small compared to the LDO pass device power dissipation and can be neglected.

The maximum continuous operating junction temperature specified for the MCP1781 is +150°C. To estimate the internal junction temperature of the MCP1781, the total internal power dissipation is multiplied by the thermal resistance from junction-to-ambient (θ_JA) of the device. For example, the thermal resistance from junction-to-ambient for the 5-Lead SOT-223 package is estimated at 68.3°C/W.

$T_{J\left(MAX\right)}=P_{LDO}\times {\theta }_{JA}+T_{A\left(MAX\right)}$

Where:

T_J(MAX) = Maximum continuous junction temperature

P_LDO = Total power dissipation of the device

θ_JA = Thermal resistance from junction-to-ambient

T_A(MAX) = Maximum ambient temperature

The maximum power dissipation capability for a package can be calculated given the junction-to-ambient thermal resistance and the maximum ambient temperature for the application. The equation below can be used to determine the package maximum internal power dissipation.

$P_{D\left(MAX\right)}=\frac{T_{J\left(MAX\right)}-T_{A\left(MAX\right)}}{{\theta }_{JA}}$

Where:

P_D(MAX) = Maximum power dissipation of the device

T_J(MAX) = Maximum continuous junction temperature

T_A(MAX) = Maximum ambient temperature

θ_JA = Thermal resistance from junction-to-ambient

$T_{J\left(RISE\right)}=P_{D\left(MAX\right)}\times {\theta }_{JA}$

Where:

T_J(RISE) = Rise in the device junction temperature over the ambient temperature

P_D(MAX) = Maximum power dissipation of the device

θ_JA = Thermal resistance from junction-to-ambient

$T_J=T_{J\left(RISE\right)}+T_A$

Where:

T_J = Junction temperature

T_J(RISE) = Rise in the device junction temperature over the ambient temperature

T_A = Ambient temperature

The internal junction temperature rise is a function of internal power dissipation and of the thermal resistance from junction-to-ambient for the application. The thermal resistance from junction-to-ambient (θ_JA) is derived from EIA/JEDEC standards for measuring thermal resistance. The EIA/JEDEC specification is JESD51. The standard describes the test method and board specifications for measuring the thermal resistance from junction-to-ambient. The actual thermal resistance for a particular application can vary depending on many factors such as copper area and thickness. Refer to Application Note AN792, “A Method to Determine How Much Power a SOT23 Can Dissipate in an Application” (DS00792), for more information regarding this subject.