Based on the analysis of the basic principle of slope compensation, a high- precision adaptive slope compensation circuit for peak current mode boost DC/DC converter is designed. The circuit dynamically detects the input and output voltage of the boost circuit to realize automatic adjustment of the compensation amount with the change of duty ratio, which makes the ramp compensation slope optimized. The design uses a high-precision subtracter to improve the accuracy of slope compensation. While eliminating sub-slope oscillation and improving the stability of boost circuit, the negative impact of compensation on boost circuit is minimized, and the load capacity and transient response speed of boost circuit are guaranteed. The circuit is designed based on SMIC 0.18um CMOS technology, with simple structure, high reliability and easy engineering implementation. Spectre circuit simulator 17.1.0.124 64b simulation results show that the circuit has high compensation accuracy and wide input and output voltage range. When the working voltage is 3.3 V, the compensation slope can be adjusted adaptively under different duty cycles, and the minimum error between the compensation slope and the theoretical optimal compensation slope is only 0.42%.
In modern power electronics systems, direct-current-to-direct-current (DC-DC) converters are widely used in mobile devices, communication systems, industrial automation, and renewable energy sources as core components for energy conversion and management. However, DC-DC converters often face a variety of disturbances and instability factors in practical applications, one of which is the slope problem. As an effective solution, precise control and stability enhancement of the DC-DC converter output voltage can be realized by introducing a slope compensation circuit.
The peak current mode control technique based on PWM modulation is widely used in DC-DC circuits due to its advantages of fast response speed, simple frequency compensation [
In this paper, an adaptive slope compensation circuit is designed for peak current control mode boost converter, according to the duty cycle change, the circuit can automatically adjust the compensation slope, avoiding the generation of subharmonic oscillations while eliminating the overcompensation phenomenon and reducing the negative impact of compensation on the system.
When the converter is controlled in peak current mode, as shown in
converges with the cycle; when the duty cycle is greater than 50%, as shown in
In
m 2 m 1 = D 1 − D (1)
From the
Δ i 1 = − m 2 m 1 ∗ Δ i 0 = − D 1 − D ∗ Δ i 0 (2)
Then after n cycles, the error due to the initial perturbation amount is:
Δ i n = ( − m 2 m 1 ) n ∗ Δ i 0 = ( − D 1 − D ) n ∗ Δ i 0 (3)
From the Equation (3), when D < 50%,the amount of perturbation to the inductor current decreases with period and decays to 0, stabilizing the system; whereas when D > 50%,the inductor current is affected by the perturbation gradually increases with the cycle, generating subharmonic oscillations, and the system’s immunity to interference deteriorates, preventing it from working stably.
In order to eliminate the subharmonic oscillations, a ramp compensation is added to the system, whose inductor current variation is shown in
Δ i 1 = − m 2 − m c m 1 + m c ∗ Δ i 0 (4)
After n cycles, the inductor current perturbation with the addition of the compensation signal is:
Δ i n = ( − m 2 − m c m 1 + m c ) n ∗ Δ i 0 (5)
In order for the inductor current perturbation to converge, it should be satisfied that:
m 2 − m c m 1 + m c < 1 (6)
The above equation reduces to:
m c > 1 2 ( m 2 − m 1 ) (7)
In boost topology [
m c > 1 2 V o u t − V i n L (8)
It can be seen that when the mc satisfies the above conditions, it is able to eliminate the subharmonic oscillations and avoid the open-loop instability that arises in the peak current control mode.
The circuit proposed in this paper is shown in
can be mainly divided into voltage acquisition module, ramp voltage generation module and reset module.
The voltage acquisition module samples Vin and Vout and converts them to current. Its circuit is shown in
V i n 1 = R 1 R 1 + R 2 ∗ V i n = V i n N (9)
V o u t 1 = R 4 + R 5 R 3 + R 4 + R 5 ∗ V o u t = V o u t N (10)
Voltage acquisition module mainly consists of three op-amps, Vin1 through the amplifier AMP1 to get VA, design take R6 = R7, can be obtained:
V A = ( 1 + R 7 R 6 ) ∗ V i n 1 = 2 V i n 1 (11)
The same reasoning applies:
V B = V o u t 1 (12)
VA is fed into the input of the amplifier AMP3, and the operational amplifier AMP3 and the transistor MN1 are connected to a voltage negative feedback structure so that VC strictly follows the variation of VA, so that the currents flowing through the resistors R8 and R9 are jointly determined by the voltages VB and VC, generating the current I1 that is correlated with the input-output voltage:
I 1 = V o u t 1 − 2 V i n 1 R 8 + R 9 = V o u t − 2 V i n R 8 + R 9 ∗ 1 N (13)
MN2 and MN1 take the same aspect ratio, hence I2 = I1, the ratio of the aspect ratio of MP1 to MP2 is 2:N. Therefore, the current Islope after the current I2 passes through the current mirror is:
I s l o p e = I 2 ∗ 1 N = 1 2 V o u t − V i n R 8 + R 9 (14)
Islope charges the capacitor Cc to produce the ramp signal Vslope [
T c = d V s l o p e d t = I s l o p e C c = 1 2 V o u t − V i n R 8 + R 9 ∗ C c (15)
Setting the appropriate values of resistors R8, R9 and capacitor Cc means that the slope compensation can be adjusted adaptively to obtain the optimal compensation slope that stabilizes the system.
From the analysis in section 2, it can be seen that the system generates subharmonic oscillations when the duty cycle is greater than 50%, so the system does not need adaptive slope compensation when the duty cycle is less than 50%, and a reset module can be added to make the slope compensation signal canceled when the duty cycle is less than 50%. Let R4 = R5, then Vout2 = 0.5 Vout1, the voltage signals Vin1 and Vout2 are connected to the positive and negative terminals of the comparator COM respectively the output signal is connected to the gate of MN3. As shown in
In the boost converter, when the duty cycle is less than 50%, the input and output voltage relationship is:
V i n > 1 2 V o u t (16)
At this time, the comparator output high level makes the reset tube MN3 on, and the slope voltage Vslope is pulled down, and no compensation signal is generated. The gate signal of MN4 is a narrow pulse signal, so that the compensation signal can be dropped quickly.
Adaptive slope compensation circuit is designed using SMIC 0.18 um CMOS process and pre-simulated in Cadence using Spectre circuit simulator 17.1.0.124 64b. The supply voltage is 3.3 Volts, the clock signal frequency is 1MHertz and the value of inductor L is 2uHenries. The circuit is simulated and verified for different input voltages, output voltages, temperatures and process angles.
When the input voltage is 3.3 Volts, the temperature is 25˚C, the process corner is tt, and the output voltage is between 8 - 15 Volts, the circuit is simulated, and the results are shown in
When the input voltage Vin = 3.3 Volts, the output voltage Vout = 12 Volts, and the process cornor is typical typical, the simulation verifies the performance of
| Output Voltage/V | Theoretical value/ (V/us) | Simulation results/ (V/us) | deviation ratio |
|---|---|---|---|
| 8 | 0.35 | 0.3613177 | 3.23% |
| 10 | 0.85 | 0.8667901 | 1.98% |
| 12 | 1.35 | 1.3657274 | 1.16% |
| 14 | 1.85 | 1.8624961 | 0.68% |
| 15 | 2.10 | 2.1088029 | 0.42% |
the slope compensation circuit at different temperatures, and the results are shown in
When the input voltage Vin = 4 Volts, the output voltage Vout = 10 Volts, and the circuit operates at 25˚C, the simulation of the slope compensation circuit at different process cornors is shown in
When the circuit operates at different output voltages, the slope compensation slope varies with the duty cycle. By setting the value of resistance, the circuit designed in this paper charges the compensating capacitor and adds the compensating voltage to the circuit when the duty cycle is greater than 50%. The comparison between the theoretical slope with the duty cycle change and the compensation slope verified by the circuit simulation in this paper is shown in
In this paper, an adaptive slope compensation circuit for PCM controlled boost DC-DC converter is designed. The circuit uses a subtracter circuit to obtain a current proportional to the voltage difference between input and output, and generates a circuit through the ramp to output a suitable compensation voltage. The simulation results show that the adaptive slope compensation circuit can adaptively change the compensation slope with the change of duty cycle, and the error with the theoretical optimal compensation slope is small, the dynamic compensation is realized, and the load capacity and transient response speed of the boost converter circuit are guaranteed. A simple temperature compensation is added to the circuit, which reduces the influence of temperature on the circuit and further improves the compensation accuracy. Influenced by the process, the ramp voltage has a slightly larger range of peak fluctuations at different process cornors, which can be corrected by trimming techniques in subsequent studies, or the circuit can be further improved to minimize the effect of the process.
The authors declare no conflicts of interest regarding the publication of this paper.
Lin, F. and Cao, X. (2023) An Adaptive Slope Compensation Circuit for Peak Current Mode of Boost Switching Power Supply. Open Journal of Applied Sciences, 13, 1730-1741. https://doi.org/10.4236/ojapps.2023.1310137