SLUS223G April 1997 – July 2022 UC1842 , UC1843 , UC1844 , UC1845 , UC2842 , UC2843 , UC2844 , UC2845 , UC3842 , UC3843 , UC3844 , UC3845
PRODUCTION DATA
Slope compensation is the large signal sub-harmonic instability that can occur with duty cycles that may extend beyond 50% where the rising primary side inductor current slope may not match the falling secondary side current slope. The sub-harmonic oscillation would result in an increase in the output voltage ripple and may even limit the power handling capability of the converter.
The target of slope compensation is to achieve an ideal quality coefficient, Q_{P} , to be equal to 1 at half of the switching frequency. The Q_{P} is calculated with Equation 37.
In Equation 37, D is the primary side switch duty cycle and M_{C} is the slope compensation factor, which is defined with Equation 38.
In Equation 38, S_{e} is the compensation ramp slope and the S_{n} is the inductor rising slope. The optimal goal of the slope compensation is to achieve Q_{P} equal to 1; upon rearranging Equation 38 the ideal value of slope compensation factor is determined:
For this design to have adequate slope compensation, M_{C} must be 2.193 when D reaches it maximum value of 0.627.
The inductor rising slope, S_{n}, at the ISENSE pin is calculated with Equation 40.
The compensation slope, S_{e}, is calculated with Equation 41.
The compensation slope is added into the system through R_{RAMP} and R_{CSF}. The C_{RAMP} is an AC-coupling capacitor that allows the voltage ramp of the oscillator to be used without adding an offset to the current sense; select a value to approximate high frequency short circuit, such as 10 nF as a starting point and make adjustments if required. The R_{RAMP} and R_{CSF} resistors form a voltage divider from the oscillator charge slope and this proportional ramp is injected into the ISENSE pin to add slope compensation. Choose the value of R_{RAMP} to be much larger than the R_{RT} resistor so that it does not load down the internal oscillator and result in a frequency shift. The oscillator charge slope is calculated using the peak-to-peak voltage of the RT/CT sawtooth waveform, V_{OSCpp}, equal to 1.7 V, and the minimum on-time, as shown in Equation 43.
To achieve a 44.74-mV/µs compensation slope, R_{CSF} resistor is calculated with Equation 44. In this design, R_{RAMP} is selected as 24.9 kΩ, a 4.2-kΩ resistor was selected for R_{CSF}.