Improve the tracking performance of the PWM voltage-controlled buck converters by using a passive pre-filter

Abstract

The voltage-controlled pulse-width modulation (PWM) scheme provides high performance, low noise, and robust operation and hence, it is a very common control method for buck converters. In this method, usually an Error Amplifier (E/A) with a Type III compensation network (i.e., PID type) is used as the controller. For applications which require tracking of the output voltage with a reference signal, the non-inverting input of the Error Amplifier (E/A) will be directly connected to the reference signal.

The method is very simple and provides very small steady-state error between the reference input and the output of the converter. However, the error can be 50% or more during fast reference transition. The peak value of this error depends on the slew rate of the reference input and compensation values. The compensation values are usually fixed and selected to achieve a stable operation and fast load transient response. Moreover, limiting the slew rate of the reference might not be possible for some applications.

To enhance the tracking performance of the PWM voltage controlled buck converter, a simple resistor-capacitor network is proposed in this article. Indeed, this network is identical to the compensation values and cancels out their effect on the tracking response of the output voltage, while having no effect on the control loop gain, stability, line- and load-regulation. The experimental result in this article confirms that using this method, the maximum tracking error of the output voltage can drop from 66% to less than 15% for a 300μs rise time of reference voltage.

Introduction

Stability, low susceptibility to noise, and fast load-transient response are usually the primary objectives in the control of synchronous buck converters. However, in many applications the output voltage of the converter should also track an eternal reference either during start-up or normal operation. The reference is often taken from another power supply, which is also providing the power to the load.

For example, the V_tt rail should follow half of the V_DDQ rail in DDR memory applications [Reference 1]. For proper operation of the load in such applications, the error between the output voltage and the reference input should not exceed certain level. However, meeting this criterion can be a challenge with a fast changing reference.

The voltage-controlled PWM method is widely used for synchronous buck converters due to its robust performance, flexibility, and low output ripple by running at constant switching frequency. Figure 1 shows a common block diagram of the synchronous buck converter with voltage mode control. In this scheme, the compensation is usually implemented with an Error Amplifier (E/A) using a resistor-capacitor network. The non-inverting input of the E/A (V_p) is connected to the external reference for tracking.

In the following section, the transfer function from the input reference to the output voltage is calculated using the average method. Then, a pre-filter circuit is proposed based on the calculated transfer function to enhance the tracking performance of the converter. Finally, simulation and experimental result are provided to confirm the effectiveness of the proposed circuit.

Figure 1: Block diagram of a voltage-mode-controlled

synchronous buck converter with tracking input

Model

Using the average-modeling technique the control block diagram of the converter can be simplified as Figure 2 [Reference 2]. In this diagram, G(s) is the transfer function of the power stage filter and is given by:

where C_o, ESL, ESR are equivalent apparent capacitance, series inductance, and resistance of the output capacitors, respectively. L is the output inductance and R_L indicated the equivalent series resistance of the power stage and can be approximated by

where DCR, R_{dson_Ctrl}, R_{dson_Sync}, and D are DC resistance of the inductor, R_ds(on) of the control-FET, R_ds(on) of the synchronous-FET, and duty cycle, respectively. Z_out is the open loop output impedance of the output filter

Figure 2: Average model of the

synchronous buck converter with tracking input.

The output of the E/A (V_e) can be expressed as

where Z_f, Z_c, A_V, R_f2 are the impedance between the output and the inverting input of the E/A, the impedance between Fb and Comp, the open loop voltage gain of the E/A, and the resistor from the inverting input to ground. Usually R_f2 is non-stuff for tracker applications and A_v>>1. Thus, Equation (4) can be simplified as

where H(s) is defined as   

Using Equations (1) to (6) and Figure 2, one can calculate the output with respect to the load current (i_o) and reference input (V_p) as

where L(s) is the loop gain and defined by

For majority of applications, the input voltage variation is less than ±10% of its nominal value. Thus, the effect of Vin on the loop gain has been neglected in the analysis in this article.

Using Equation (7) the control block diagram of the converter is simplified as Figure 3.

Figure 3: Control of a synchronous buck converter

using a compensation network and a pre-filter.

Compensation values are primarily selected to make the loop gain with a bandwidth of 1/5th to 1/10th of the switching frequency and a phase margin of over 45 degree to provide robust stability and fast response to step load transient (Figure 4). On the other hand, 1/H(s) should be less than -20db for a good fidelity of the output voltage to the tracking input. This latter condition is not valid for most of applications.

The compensation network has an integrator to reduce the steady state error to the reference input. Thus, 1/H(s) acts as a differentiator before the first zero of the compensator (F_z1). This behavior can explain the overshoot on the output during fast reference variation. However, at frequencies much lower than F_z1, where |1/H(s)|<<0 and |L(s))>>0, the output voltage tracks the reference input perfectly. Above F_p3, the gain of 1/H(s) increases linearly with the frequency.

Thus, any high-frequency noise at the tracking input can create jitter on the inductor node (also called the switch node) signal and extra output voltage ripple. To avoid these effects, we propose using a pre-filter at the reference input of the E/A. The pre-filter with this configuration doesn’t affect the stability of control loop. Thus, the problem of tracking and loop stability can be solved independently.

Figure 4: The gain of H(s) and 1/H(s)

for a Type-III compensator.

Pre-filter Design

One choice of pre-filter to achieve a good tracking performance is the inverse of (1+1/H(s)). That is,

This filter can be realized as shown in Figure 5, which has the same values as the compensation network.

Figure 5: The proposed pre-filter to enhance the

tracking performance of buck converter.

At frequencies lower than the loop bandwidth, where |L(s)|>>1, using this network the output of the controller can track the input with minimal error. Above the control loop bandwidth, the loop gain (|L(s|) drops and so the output voltage response to the tracking input. Thus, the network of Figure 5 can be simplified since its high frequency poles and zeros don’t have any significant effect on the tracking performance of the converter.

 One possible solution is removing C_c2, and replacing R_f3 with short circuit. One can further simplify the circuit by replacing Z_f with a single resistor and Z_c with a single capacitor and placing the corner frequency of this filter at F_Z1.