L6258 datasheet(11/18 Pages) STMICROELECTRONICS

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AloopdB = AxdB + BxdB

Ax|dB = ACpw|dB + ACload|dB

and

Bx|dB = ACerr|dB + ACsense|dB

this means that Ax|dB is the sum of the power am-

plifier and load blocks;

Ax|dB = (29,5) + (-31.4) = -1.9dB

The BODE analysis of the transfer function of Ax

is:

The Bode plot of the Ax|dB function shows a DC

gain of -1.9dB and a pole at 163Hz.

It is clear now that (because of the negative gain

of the Ax function), Bx function must have an high

DC gain in order to increment the total open loop

gain increasing the bandwidth too.

Error Amplifier and Sense Amplifier

As explained before the gain of these two blocks

is :

BxdB = ACerrdB + ACsensedB

Being the voltage across the sense resistor the

input of the Bx block and the error amplifier volt-

age the output of the same, the voltage gain is

given by :

ib = Vsense

⋅ Gs = Vsense ⋅

Verr_out = -(ic

⋅ Zc) so ic = -(Verr_out ⋅

)

because ib = ic we have:

Vsense

⋅

= -(Verr_out

⋅

)

= −

Verr_out

Vsense

= −

In the case of no external RC network is used to

compensate the error amplifier, the typical open

loop transfer function of the error plus the sense

amplifier is something with a gain around 80dB

and a unity gain bandwidth at 400kHz. In this

case the situation of the total transfer function

Aloop, given by the sum of the AxdB and BxdB is :

The BODE diagram shows together the error am-

plifier open loop transfer function, the Ax function

and the resultant total Aloop given by the follow-

ing equation :

AloopdB = AxdB + BxdB

The total Aloop has an high DC gain of 78.1dB

with a bandwidth of 15KHz, but the problem in

this case is the stability of the system; in fact the

total Aloop cross the zero dB axis with a slope

of -40dB/decade.

Now it is necessary to compensate the error am-

plifier in order to obtain a total Aloop with an high

DC gain and a large bandwidth. Aloop must have

enough phase margin to guarantee the stability of

the system.

A method to reach the stability of the system, us-

ing the RC network showed in the block diagram,

is to cancel the load pole with the zero given by

the compensation of the error amplifier.

The transfer function of the Bx block with the

compensation on the error amplifier is :

= −

− j

π ⋅ f ⋅ Cc

In this case the Bx block has a DC gain equal to

the open loop and equal to zero at a frequency

given by the following formula :

Fzero

π ⋅ Rc ⋅ Cc

L6258

11/18

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