Equation derivation

TN0024

2/11

1

Equation derivation

The equation derivation approach is to determine the minimum bulk voltage with energy

equations and then use the energy at this voltage to determine the minimum operating

voltage. The symbol for overall efficiency is cc and the efficiency used when the AC line is

2

MathCAD

MathCAD is used to determine the minimum operating voltage and also to determine the

as a blue dashed line and the equivalent DC input voltage in red. Note that for a bulk

capacitor of 60

µF (x-axis), the DC voltage is about 80 V (y-axis). A procedure to calculate

the bulk DC voltage or the bulk capacitance is given in Section 6.1., Equation 27 and

Equation 28.

3

P-SPICE

A P-Spice simulation of a bulk capacitor discharge can be approximated using a voltage

controlled current source G1 (see Figure 2). Using an effective voltage range from the peak

bulk voltage to a minimum operating voltage, a load current can be simulated which is

inversely proportional to the bulk DC voltage.

voltage turn off with a 10ms HOLD - UP time requirement and a power supply output power

of 24 W. The following equations calculate the bulk capacitor current supplied to the power

supply at 150 V and 80V for an output power of 24 W and an efficiency of 87%:

Equation 1

Equation 2

Equation 3

Equation 4

A voltage controlled current source with a 230 V reference can be used with a gain of

0.0023 to simulate the above currents.

P

o

24W

=

N0.87

=

P

in

P

o

N

------

24

0.87

-----------

27.6W

=

=

=

Vc

150V

=

I

C

27.6

150

-----------

0.184A

=

=

at

Vc

80V

=

I

C

27.6

80

-----------

0.345A

=

=

at

µ