ISL95873

9

FN8390.0

December 10, 2012

The R4™ modulator is an evolutionary step in R3™ technology.

Like R3™, the R4™ modulator allows variable frequency in

response to load transients and maintains the benefits of

current-mode hysteretic controllers. However, in addition, the

R4™ modulator reduces regulator output impedance and uses

accurate referencing to eliminate the need for a high-gain

voltage amplifier in the compensation loop. The result is a

topology that can be tuned to voltage-mode hysteretic transient

speed while maintaining a linear control model and removes the

need for any compensation. This greatly simplifies the regulator

design for customers and reduces external component cost.

Stability

The removal of compensation derives from the R4™ modulator’s

lack of need for high DC gain. In traditional architectures, high DC

gain is achieved with an integrator in the voltage loop. The

integrator introduces a pole in the open-loop transfer function at

low frequencies. Thus, combined with the double-pole from the

output L/C filter, creates a three pole system that must be

compensated to maintain stability.

Classic control theory requires a single-pole transition through

unity gain to ensure a stable system. Current-mode architectures

(includes peak, peak-valley, current-mode hysteretic, R3™ and

R4™) generate a zero at or near the L/C resonant point,

effectively canceling one of the system’s poles. The system still

contains two poles, one of which must be canceled with a zero

before unity gain crossover to achieve stability. Compensation

components are added to introduce the necessary zero.

Figure 8 illustrates the classic integrator configuration for a

voltage loop error-amplifier. While the integrator provides the

high DC gain required for accurate regulation in traditional

technologies, it also introduces a low-frequency pole into the

control loop. Figure 9 shows the open-loop response that results

from the addition of an integrating capacitor in the voltage loop.

The compensation components found in Figure 8 are necessary

to achieve stability.

Because R4™ does not require a high-gain voltage loop, the

integrator can be removed, reducing the number of inherent

poles in the loop to two. The current-mode zero continues to

cancel one of the poles, ensuring a single-pole crossover for a

wide range of output filter choices. The result is a stable system

with no need for compensation components or complex

equations to properly tune the stability.

Figure 10 shows the R4™ error-amplifier that does not require an

integrator for high DC gain to achieve accurate regulation. The

result to the open loop response can be seen in Figure 11.

FIGURE 7. ISL95873 VOLTAGE PROGRAMMING CIRCUIT

SREF

+

-

EA

+

-

FB

FIGURE 8. INTEGRATOR ERROR-AMPLIFIER CONFIGURATION

V

INTEGRATOR

FOR HIGH DC GAIN

COMPENSATION TO COUNTER

INTEGRATOR POLE

FIGURE 9. UNCOMPENSATED INTEGRATOR OPEN-LOOP RESPONSE

f (Hz)

p1

p2

p3

L/C DOUBLE-POLE

INTEGRATOR POLE

z1

ZERO

-20dB CROSSOVER

REQUIRED FOR STABILITY

COMPENSATOR TO

ADD z2 IS NEEDED

CURRENT-MODE