AN1882 datasheet(18/30 Pages) STMICROELECTRONICS

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Application information

AN1882

18/30

Doc ID 10209 Rev 4

5.1.4

Compensation network (R1C3)

As it is shown in the

Section 3.2 the system stability can be studied with the loop transfer

function given by the

Equation 3Equation 3. If the output capacitor is a ceramic type the zero

due to the ESR generally will be out of the system bandwidth, so the stability of the system

will be ensured by the cancellation between the pole due to the output capacitor and the

equivalent load and the R1C3 zero. In the Equation 15Equation 15, a simplified gain loop

expression, valid around the transition frequency fT is given by:

Equation 15

Supposing C2 = 22 µF, the transition frequency at 0 dB equal to 30 kHz (fT is equal to the

system bandwidth), and the output voltage equal to 1.8 V the R1 value can be calculated as:

Equation 16

The nearest standard E12 series value is R1 = 47 kΩ.

The higher is the bandwidth, the faster will be the transient response but the bandwidth (and

so the R1 value) must be lower than fSW/10 to avoid the effect due to the sampling effect

poles as mentioned in the

Section 3.2. The zero due to the compensation network must be

at the least 5 times before the frequency transition, so the C3 value will be:

Equation 17

The nearest standard value is C3 = 470 pF. If the output capacitors are tantalum type the

ESR zero is in the system bandwidth and it can be used to stabilize the system so the zero

due to the compensation network will be useless (the C3 is necessary to the integrator

function).

5.2

Losses and efficiency

There are losses affecting the efficiency of the application. Some of these losses are related

to the device and others are related to the external components. The most important losses

are listed below.

5.2.1

Conduction losses

These losses are basically due to the not negligible resistances of the internal switches and

the external inductor. Usually the current ripple across the inductor is negligible and so to

estimate the conduction losses of the inductor, the average output current can be

considered. The conduction losses of the switches depend also on the duty cycle of the

application. The RMS current flowing through the high side MOSFET is (IO)

2 · D while the

RMS current flowing through the low side MOSFET is (IO)

2 · (1-D). So, the total conduction

losses are:

LOOP s

()

mR1α

-------------------

πf

TC2

mα

-------------------

πf

TR1

-------------------

500pF

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