RC network connected between the output and

the negative input of the same.

For the evaluation of the stability of the system,

we have to consider the open loop gain of the

current control loop:

Aloop = ACerr

⋅ ACpw ⋅ ACload ⋅ ACsense

where AC... is the gain of the blocks that refers to

the error, power and sense amplifier plus the at-

tenuation of the load block.

The same formula in dB can be written in this

way:

So now we can start to analyse the dynamic char-

acteristics of each single block, with particular at-

tention to the error amplifier.

Power Amplifier

The power amplifier is not a linear amplifier, but is

a circuit driving in PWM mode the output stage in

full bridge configuration.

The output duty cycle variation is given by the

comparison between the voltage of the error am-

plifier and two triangular wave references Tri_0

and Tri_180. Because all the current control loop

is referred to the Vr reference, the result is that

when the output voltage of the error amplifier is

equal to the Vr voltage the two output Out_A and

Out_B have the same phase and duty cycle at

50%; increasing the output voltage of the error

amplifier above the Vr voltage, the duty cycle of

the Out_A increases and the duty cycle of the

Out_B decreases of the same percentage; on the

contrary decreasing the voltage of the error ampli-

fier below the Vr voltage, the duty cycle of the

Out_A decreases and the duty cycle of the Out_B

increases of the same percentage.

The gain of this block is defined by the amplitude

of the two triangular wave references; more pre-

cisely the gain of the power amplifier block is a re-

versed proportion of the amplitude of the two ref-

erences.

In fact a variation of the error amplifier output volt-

age produces a larger variation in duty cycle of

the two outputs Out_A and Out_B in case of low

amplitude of the two triangular wave references.

The duty cycle has the max value of 100% when

the input voltage is equal to the amplitude of the

two triangular references.

The transfer function of this block consist in the

relation between the output duty cycle and the

amplitude of the triangular references.

=

2

Triangular Amplitude

= 20 ⋅ log

2

⋅ 24

1.6

Moreover, having the two references Tri_0 and

Tri_180 a triangular shape it is clear that the

transfer function of this block is a linear constant

gain without poles and zeros.

Load Attenuation

The load block is composed by the equivalent cir-

cuit of the motor winding (resistance and induc-

tance) plus the sense resistor.

We will considered the effect of the Bemf voltage

of the motor in the next chapter.

The input of this block is the PWM voltage of the

power amplifier and as output we have the volt-

age across the sense resistor produced by the

current flowing into the motor winding. The rela-

tion between the two variable is :

=

so the gain of this block is:

ACload

=

=

12

31.4dB

where:

equivalent resistance of the

motor winding

sense resistor

Because of the inductance of the motor LL, the

load has a pole at the frequency :

Fpole

=

1

2

π ⋅

Fpole

=

1

6.28

⋅

12

12

= 163Hz

Before analysing the error amplifier block and the

sense transconductance block, we have to do this

consideration :

L6258

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