Current Sensor and Slope Compensation Circuit

SIDBHO uses current programming mode [43] which has the advantage of fast transient, low ripple and easier in system compensation comparing to voltage mode [43]. The approach to implement current programming mode is to apply current sensor which have various types such as putting sensing resistor near inductor to copy current directly [44]; using parallel

external components of sensing capacitor and resistor to re-bulid inductor current slope [44];

and applying sensing mosfet for each PowerMOS [44].

The merit of putting sensing resistor in the left or right terminal of inductor is accurate because of the capability of making a full copy of inductor slope, but may be in the problem of limited bandwidth due to the use of operational amplifier and energy waste in use of resistor. The advantage of using parallel sensing capacitor and resistor is also accurate since the tunable of external elements, but in the difficulty of delay condition and large area consumption. The drawback of applying sensing mosfet for PowerMOS is not so accurate comparing with the previous cases, but in the great properties of easier implementation and much smaller area occupation, moreover, the flexibility of choosing any PowerMos sensed you want. The last approach will be applied due to its merits and the detailed operating principles is in next paragraph.

V^DD Fig. 27. Current Sensor Circuits.

The dashed green line in Fig. 27 is current sensor whereas outside are the energy delivery elements. As mentioned in last paragraph, the purpose of using sensing mosfet for PowerMOS is an economic way to go and next the determination of which side should be considered. It’s very inappropriate to sense M_sw1 in the left side of inductor since V_X1 would face negative voltage problem that it’d better to be avoided in control circuits, or the layout of circuits is very complicated and it seemes to be in the result untouchable in the left side of inductor. Alternatively, the use of Msw2, Msw3 is better which deicides the 1^st transition point composited by V_sum, V_epn with M_sw2 sensed and the 2^nd transition point composited by V_sum, V_ep with Msw3 sensed in Type II in Table IV. But it’s in the problem of requirement in blanking circuit to prevent error switching when the discontinuousness of sensing M_sw2 and sensing Msw3. Thus, to coincide with choosing Type V in previously, the reason for flyback first and boost later has the merit to sense M_sw2 only to decide both transition points because of the continuousness among 1^st and 2^nd path.

In Fig. 27, M₁, M₂, M₃, M₄ and M₅ use current mirror topology and provide current bias for others. The path concluding M6 M7 and M8 form a simple negative closed loop to force V_XN varying with V_X2 and copy the sensing current I_sense which is M-times smaller than I_L induced by the size difference of Msw2 and Msesne. Finally, M9, M10 and M11 pass the sensing current Isense through sensing resistor and V_s is generated. And the formula reconstruct inductor current:

SENSE L

SENSE SENSE

S

I R

R M I

V 

^

 1

^{ }

(15)

IL = 400mA ~ 600mA I^L = 0mA ~ 200mA

Vsense Vsense

IL IL

Slope = 0.427 Slope = 0.45

Fig. 28. Simulation Results in Current Sensor Circuits.

In the simulation result in Fig. 28, from the slope calculation, the accurate of Vsense is acceptable when I_L varies from 0~200mA to 400mA~600mA range.

The current programmed controller is unstable when converter operates above 50% duty cycle without compensation that shows in Fig. 29. The unstable problem called as sub-harmonic oscillation phenomena. In other words, the perturbed quantity of inductor current was large more and more during a few periods. The phenomena also occurred in other topologies such as boost and buck-boost converters. To avoid this stability problem, the control scheme is usually modified by adding an artificial ramp to the sensed current in the following descriptions.

Fig. 29. Inductor Current at Stable and Unstable Oscillation in Current-Mode Converter.

The steady-state and perturbed waveform of inductor current are illustrated in Fig. 30.

We can explain the phenomena of steady-state waveform and perturbed waveform with

derived formula. The steady-state waveform of inductor current with m1 slope ramps up in first interval and ramps down with m₂ slope in second interval. When the perturbed waveform of inductor current occurred with dT^ˆ _s, the current difference was introduced in m dT₁ ^ˆ _s[45], [46].

The slope of inductor current equals:

According to Fig. 30, we can derive:

In steady-state, the above equation i_L(0)i T_L( )_s and shows as:

From Fig. 30, we can use the steady-state waveform to express the current difference

ˆ (0)_L

i i Tˆ ( )_{L s} as the slope multiplied by the interval length, Hence:

Elimination of the intermediate variable ˆd from equation(19) leads to:

Fig. 30. The Perturbation Waveform of Inductor Current.

1

V

ⁱⁿ

V

^out

,

2

V

^out

m m

L L

  

(16)

2 1 2

( ) ( ) (0)

L s L s s L s s

i T i DT m D T i m DT m D T (17)

' 2

1 2 '

1

0

_{s s}

, : m D

m DT m D T then

m D

  

(18)

1ˆ 2 ˆ

ˆ_L(0) _s , ( )ˆ_{L s s}

i  m dT i T m dT (19)

A similar analysis can be performed during the next switching period, show that:

After n switching periods, the perturbation becomes:

Note that, as n tends to infinity, the perturbation i nTˆ (_{L s}) tends to zero provided that the characteristic value –D/D’ has magnitude less than one. Conversely, the perturbation i nTˆ (_{L s})

becomes large in magnitude when the characteristic value  D D^' has magnitude greater than one. Hence, for the stable operation of the current mode controller, we need D/D’<1 or D<0.5.

The stable situation with compensation ramp is presented in Fig. 32. When the converter operates with D<0.5, the perturbation inductor current will lead to be stable. Conversely, the perturbation inductor current will lead to be unstable to cause the sub-harmonic oscillation if converter operates with D>0.5 and no compensation.

The sub-harmonic oscillation is a well-known problem of current-mode controller.

However, the converter can be stable at all duty cycles by adding the compensated ramp to the sensed inductor current as shown in Fig. 31. This compensated ramp has the qualitative effect of reducing the gain of the current sensing feedback loop to solve the unwanted oscillation problem in current-mode controller of dc-dc converters.

2

Fig. 31. Current-Mode Control Signal with the Compensation Ramp and Inductor Current.

The compensation theorem is represented in Fig. 31, the perturbation iˆ (0)_L and i Tˆ ( )_{L s}

can express in terms of the m₁, m₂, m_aand the dT^ˆ _s as follows:

Fig. 32. Steady-State and Perturbed Inductor Current Waveforms with Compensation.

Elimination of dT^ˆ _s yields:



1



ˆ (0)

_L

ˆ

_{s a}

i   dT  m  m

(24)



2



ˆ ( )

_{L s}

ˆ

_{s a}

i T   dT  m  m

(25)

2 1

ˆ_L( )_s ˆ_L(0) ^a

a

m m i T i

m m

  

     ⁽²⁶⁾

A similar analysis can be used to the n^th period, leading to:

For larger n periods, the perturbation magnitude i nTˆ (_{L s}) tends to equations(22).

Therefore, for stability of current mode controller in CCM, it needs to choose the slope of the artificial ramp m_a such that the characteristic value  has magnitude less than one.

Conversely, the perturbation i nTˆ (_{L s}) becomes larger when the characteristic value  has magnitude greater than one:

One common choice of the compensation ramp slop is

This compensation ramp results in the characteristic valueto become zero for all duty cycle of the converter. Therefore, i Tˆ ( )_{L s} is leading to zero for anyiˆ (0)_L . Besides, another common choice of m_a is:

The above characteristic causes the value  to become zero for all duty. As a result,

ˆ ( )_{L s}

i T is zero for any iˆ (0)_L . This behavior is known as deadbeat control when the system corrects all errors after one switching period. And the compensated inductor current shows in Fig. 33.

2 2

1 1

ˆ ( ) ˆ (( 1) ) ˆ (0) ˆ (0)

n

a a n

L s L s L L

a a

m m m m

i nT i n T i i

m m m m 

     

             (27)

ˆ (_{L s}) 0 1 i nT  when





(28) ˆ (_{L s}) 1

i nT   when  

2 2

1m

m_a  (29)

2

m

a

 m

(30)

4.2 System Compensation Technique

在文檔中 應用於膽固醇液晶顯示器之單電感雙極性正負高壓輸出直流直流電源轉換器 (頁 51-59)