The Quasi-Resonant Family of Converter Topologies
Examples of Quasi-Resonant Topologies
The conversion ratio also depends on the load in the case of a half-wave switch. 2.2 (b) the half-wave switch has the desirable property of producing a conversion ratio that is nearly independent of the load.
Control of Quasi-Resonant Converters
The switching waveforms have the same shapes as those of the zero current converters in fig. The switch must be turned on again at a time determined by the development of the resonant switch waveforms.
Previous Methods of Analysis
In the DC analysis, the non-resonant reactances of the converter are assumed to have a small ripple. Topological rules are derived that govern the relationship of the PWM switch to the reactances in the converter.
Switching in PWM Converters
When each device is on, it carries current ion and when it is ON it is subjected to a voltage Voff∙ Device currents are constant during the turn-on time because they are supplied by a constant current source - one or more "solids". This value is Ion, and the voltage across the diode, with the transistor still on, is Vroff∙ For example, in the PWM buck converter of Fig.
Resonant Switches
This is the advantage of the resonant zero-current switch: the switch S can be turned OFF when = 0, dramatically reducing switching losses and allowing operation at much higher frequencies. When the current in the switch S reaches zero, the diode Pi turns off and the resonant circuit is "broken".
The Small-Ripple Approximation
Capacitors at the input or output have little ripple due to the nature of the DC input and output voltages.). The magnitudes of reactances required to attenuate these drive waveforms to produce a small ripple in Ion and Voff are therefore comparable between PWM and quasi-resonant converters operating at the same power level, load, and switching frequency.
Averages of the Resonant-Switch Waveforms
In a quasi-resonant converter based on this PWM topology, the conversion ratio M is the same function of the ratios ιs∕Iaa and v∑>fVoκ. References [4,7,8] contain analyzes of the dc behavior of buck, boost, and buck-boost quasi-resonant converters.
Relation to PWM Conversion Ratio
Output Resistance
Note that D,p {M} is not 1 — Pp(ΛΓ).) The derivative G,(p) is negative while Dp(Af) is positive, so Rout is positive as expected. The output resistance of a half-wave quasi-resonant buck converter is a significant part of the load resistance, especially for low values of MRq∕R, or equivalently p.
Modelling Goal
For a non-linear load - one that is not a linear resistor - the values of Rl and R can be quite different. This approximation allows one to check its small-signal behavior by measuring the frequency response—the magnitude-phase relationship of the fundamental component of the system's output with respect to. By restricting consideration to a specific class of converters—those with single switches and no coupling—the analysis of this work was able to apply the topology and behavior of the PWM converter to its quasi-resonant offspring, yielding general expressions for the DC conversion ratio and small-signal coefficients.
First, it introduces in Section 10.1 the elements of a single-phase ac-dc power conversion system and lays out conventions and definitions for later use. When t∕ contains harmonics other than the fundamental—harmonics that cannot contribute any average power—distortion. Since the current is not zero when the rectifier bridge switches, at θ = 0 and 0 = π, the line current is discontinuous.
12.4(d) the distortion of the current increases, but at the same time the displacement factor decreases. 12.8(d), the filter picks up the narrow pulses characteristic of the capacitor input filter or the low Kι inductor input filter.
A Low-Prequency Model for the Resonant Switch
Small-Signal Circuit Model
The perturbations of the continuous averages of equations (5.3) and (5.4) are functions of ιon, υoff, and fs, the latter being a small-signal variation of the control variable Fs. For example,. All quantities in the rest of the circuit are replaced by their small-signal variations, including 7on and Voff, which are replaced by ιon and υoff. ∙ The frequency variation fs is considered an independent parameter, and the sources for it. It should be noted that the resistance Rl appearing in the small-signal model of Fig.
The R value that appears in the dc equations and small-signal parameters is the ratio V/1, the dc resistance of the load.
Interpretation of the Small-Signal Model
By a similar process, the voltage source Λt,∙tθn can be replaced by two sources, one in the ion branch and one in series with the current sources from the switch S, as in Fig. The cross term, (Λ,∙, ∙ — Λvv)υoffto∏, can add to or subtract from the power dissipated in the resistors. The damping introduced by the half-wave resonant switch is a common feature with PWM converters operating under either current-mode or off-mode programming.
The damping in current mode programming is visible in the circuit model of [15] as a resistor in series with the inductor whose current is limited.
An Example
Therefore, the circuit model is reciprocal (except for independent sources) and lossless. If, instead of a half-wave switch, the buck converter was equipped with a full-wave resonant switch, then the small-signal model would follow Fig. Since Λ,∙,∙ = huυ = Fs/Fo, the two dependent sources can be combined into a transformer and the circuit rearranged as in Fig.5.11(b).
This circuit is known as the circuit model obtained by state space averaging [11], with D replaced by Fs/Fq and d similarly replaced by }s∕Fq.
Effects of the Resonant Reactances
Then, using the dual of Definition 2, the behavior of the zero-voltage resonant switch can be derived in an equally general way as for the zero-current switch. The resulting dual converter can be developed by applying duality at each step of the PWM to quasi-resonant converter transformation. This expression, valid for all quasi-resonant ZVS converters, allows drawing the dc characteristics.
When duality is applied to the small-signal alternating current model, the subscripts of the h-parameters must be changed in addition to the transformations in Table 6.2.
Multiple Conduction Cycles
Converters with Transformers
Another approach is given here which gives particularly simple relationships when the resonant inductor and capacitor are on opposite sides of the transformer. The diode then converts the alternating current from the transformer back into direct current corresponding to the load. Let the transformer have a turns ratio of 1:2 V so that the (secondary) voltage on the load side is N times higher than the (primary) voltage on the source side.
If Lτ and Cr happen to be on the same side of the transformer, one of these elements must be reflected across the transformer and the resulting value used in the definition of Rq.
Converters with Multiple Switches
The presence of the resistors indicates the ever-present damping effect of the half-wave switch. The purpose of this section is to demonstrate that con. the version ratio is independent of the position of the resonant elements. As might be expected, the conversion ratio is always slightly less than the predicted value due to losses in Rι, the resonant tank, and ON losses of the transistor and diodes.
Measurements of the conversion ratio of the other two variations of the converter yielded values almost identical at each operating point.
Small-signal Measurements
Frequency response, however, is only concerned with the component of the output waveform at the modulation frequency. The voltage controlled oscillator (VCO) modulates the switching frequency under the control of the ve signal. In a PWM buck converter, increasing the load resistance would increase the loaded Q of the output filter, leading to a poor frequency response.
In short, the half-wave switch damping is not useful in removing the zero right half plane in the ZVS boost converter.
Modulators for Frequency-Controlled Converters
One of the most common power converters is the AC-DC converter, which supplies a DC load with power from an AC source. The complexity of modern systems also makes them more sensitive to line voltage quality. 10.1) and is the ratio of the DC load voltage to the peak sinusoidal line voltage.
The waveforms on the line side of the rectifier are periodic with period 7}, as shown in the sample waveforms of Fig.
The Capacitor-Input Filter
In words, power factor is the ratio of average power (also called real, real, or active power) to volt-amps (VA). Power factor is therefore a measure of how efficiently a device uses its rms input current. The Cauchy-Schwartz inequality implies that the maximum power factor arises when the Une current ή is proportional to the line voltage υ∣.
If the line voltage is distorted, then the line current must and must be distorted to achieve unity power factor.
Other Measures of Current Quality
In linear loading, the mains current contains only a fundamental component and the power factor is given solely by the displacement factor, a well-known result for motors and other reactive loads. Distortion can be more difficult to correct, depending on the frequency of the offending harmonic components. In the case of distorted (non-sinusoidal) line currents, the frequency and relative magnitudes of the unwanted harmonics are important factors.
High-frequency components of the input current can also be important in the time domain.
Sine Wave or Proportional Current?
The inductor promotes the continuity of the input current, broadening the short pulses drawn by the capacitor input filter and increasing the power factor. The output voltage V of the inductor-input filter is assumed constant for analysis purposes. The rms value of the line current is the same as the rms value of ia,.
Distortion is small, but the phase shift of the base keeps the power factor relatively low.
Resonant-Input Filter
As with the inductor-input filter, the power factor and conversion ratio are functions of the individual parameter. Unlike the inductor input filter, however, the series inductance of the series resonant filter ensures that the line current is always continuous. The fundamental components of the line voltage and the square wave from the bridge must cancel in magnitude and phase to ensure finite currents in the resonant circuit.
The major disadvantages of the resonant input filter are the large size of the reactive elements and the large rms current in both capacitors.
Ferroresonant Transformer
Therefore, the ferro adjusts the output voltage against changes in line voltage amplitude and waveform. The resonant L-C circuit gives the ferro a second-order forward voltage gain with a large resonant peak, assuming that the saturation transformer and the load present an impedance much greater than the characteristic impedance of the resonant circuit. It is unlikely that ferro will be used specifically as a means of shaping the input current.
However, when selected as a means of regulating against line voltage spikes and variations, the ferro provides a significant improvement in current waveform and power factor over a capacitor input filter.
Tuned Filters
For comparison, consider the stored energy of the elements of the resonant input filter in Section 12.2. At low switching frequencies, the filter is usually on the line side of the bridge rectifier. In other words, the input current distortion factor is not improved by faster switching.
These values are all ideal, and neglect the effect of the input filter as well as any disturbances in the line voltage.
Boost-Based Topologies
The line current is discontinuous at the intersection of the input voltage sine wave unless Kι is low. Instead of tracking the rectified sinusoidal reference, the input current ig is kept constant by active switch control. Due to the symmetry of the current pulses within half a cycle of the mains voltage, the input current does not suffer from a phase shift.
In the boost converter, the input current contains both halves of the inductor current pulse, rather than just the rising half as in the buck and flyback converters.
Necessary Conditions for Shaping
Automatic Current Shaping
Resonant Converters as Shapers
Energy Storage Methods
Implications of Stored Energy
Isolation
