Self oscillating PWM modulators , a topological comparison

High precision control of the output voltage or current of a switch mode converter with fast response is required for a number of applications. Dependent on the type of application, the desired precision and transient response can be difficult, if not impossible, to achieve with standard Pulse Width Modulation (PWM) control caused by limitations in dynamic capabilities which often limits fast tracking of a reference signal, or fast settling during load steps due to too small achievabIe control loop bandwidth. Achievable open loop bandwidth for standard voltage and current mode PWM modulators is typical in the fJl0 or fJn range respectively, where f, is the switching frequency of the converter. For some applications this will require unacceptable high switching frequency to achieve enough control loop bandwidth for the desired dynamic performance. With self oscillating modulators, the open loop bandwidth is equal to f, which makes this trpe of modulators an excellent choice for a wide range of applications. Self oscillating P W M modulators can be made in a number of ways, either as voltage or current mode modulators, and the self oscillating behavior can be achieved either by using hysteresis control or by shaping the open loop function of the modulator so its gain and phase response causes a closed loop natural oscillation. The two main types of self oscillating modulators have many similarities, but differences in dynamic performance and linearity are present. The work presented is related to the author's work with switch mode audio power amplifiers, where linear tracking of the reference signal is of major importance. Use of the modulator topologies presented are not limited to this kind of equipment, but can be used in a very wide range of appIications kom very low to very high power levels. I. lst ORDER SELF OSCILLATZNG MODULATORS Self oscillating modulators use no externally generated carrier signal fed into a comparator, but are basically a closed loop circuit with gain and phase characteristics that ensures a closed loop oscillation. That means Om-open loop gain at the frequency where the phase shifl of the open loop function is -130'. 1" order self oscillating modulators are characterized by an open loop gain function as an integrator, which by itself results in -90" of phase shift. The phase response is modified by introducing a time delay, which is equal to a linear phase shift. The oscillation starts automatically when the additional phase shift caused by the time delay approaches -900. B. Hysteresis modulators email: spo@oersted.dtu.dk email: ma@oersted.dtu.dk 0-7803-8S86-1/04/$20.00 02004 IEEE 403 Figure 1 Current mode hysteresis modulator Figure 1 shows a basic current mode hysteresis modulator [l]. The inductor current is the integral of the difference between the output voltage of the power stage and the output voltage. The measured value of the inductor current is subtracted from the reference voltage, and fed into a hysteresis window to generate the P W M signal. Since the reference voltage controls the low frequency part of the output current, the modulator is a voltage controlled current source. The hysteresis window adds a controlled time delay equal to: td = vm (1) where Vb, is the height of the hysteresis window and bm is the gradient, or slope, of the carrier. Figure 2. Current mode hysteresis modulator, inductor current and carrier waveform, M 4 . 5 Figure 2 shows inductor current and carrier wavefom for the current mode hysteresis modulator in Figure 1 with a modulation index, M, of 0.5 . The modulation index is the ratio between output voltage and power supply voltage. At zero output, the carrier waveform is a pure triangle, but at higher M, the carrier waveform change into a sawtooth shaped signal. This is due to the integration made by the inductor of the voltage across it. Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on February 17,2010 at 05:28:13 EST from IEEE Xplore. Restrictions apply. As it is seen in Figure 2, the switching frequency drops at high M due to the integration of a smaller voltage across the inductor, resulting in a flatter slope of the carrier signal, giving a greater time delay, before the threshold of the hysteresis window is met, thus reducing the fiequency where the -180" of phase shift is met. The switching fiequency of the current mode hysteresis modulator is given by: where VS is the power supply voltage, Ihyg is the height of the hysteresis window, L the inductor value and the time delay trough the modulator loop. It is seen that if the height of the hysteresis window is made from the power supply rails, the switching fiequency will be independent of the value of the supply rails. At higher M, the carrier shape deviates from straight slopes as illustrated in Figure 3. Figure 3. Current mode hysteresis modulator, output voltage, inductor current and carrier waveform, M=O.S Since the slope of the carrier is the integral of the voltage across the inductor, the slope is sensitive to the ripple voltage on the output of the modulator. When the switchmg frequency drops, the output ripple voltage gets comparable to the inductor voltage, and the slope of the carrier becomes smaller, degrading the performance of the modulator. In most applications the maximum modulation index of the modulator should be limited to appr. 0.8, keeping a minimum switching frequency and thereby keeping a good performance. where ?ht is the time constant for the integrator, and vhpt is the height of the hysteresis window. The voltage mode hysteresis modulator has the same dependence of the modulation index as for the current mode hysteresis modulator. . . .__, . , . Figure 5. Voltage mode hysteresis modulator, power stage output voltage, carrier waveform and reference, M4.5 D. 1" orderjsced delay selfoscilZdng modulators A 1" order fixed delay modulator can easily be implemented by removing the hysteresis block in a hysteresis modulator. The additional -90" of phase shift to start the oscillation will be determined by the time delay of the modulator loop only, thus giving the switching fiequency: Figure 6. Self oscillating modulator with propagation delay control of switching fiequency, power stage output voltage, carrier waveform and reference, M=0,5 As it is seen in Figure 6, the carrier signal correspond to the carrier signal of the hysteresis modulators, except that it is summed with the reference voltage, but the switching fiequency's dependence on M is the same as for the hysteresis modulators. E. d' order selfosciIIut2ng modulators Open Loop 1 runcton Figure 7. Block diagram of COM modulator Figure 7 shows the COM, Controlled Oscillation Modulator [3]. The open loop function is shaped with a dominant low frequency pole, resulting in -90° phase shiR at high frequencies. Two additional high fiequency poles