On the Use of a Common Smoothing Choke in a Stabilized Voltage Converter
Abstract Generated abstract
This paper examines multichannel stabilized DC voltage converters in which separate output filter chokes are replaced by a single multiwinding smoothing choke. It presents a calculation procedure for the common choke, including stored energy, winding turns, inductance, air gap, and distribution of output filter capacitance, and argues that winding ratios should be based on transformer turns rather than output voltages to account more accurately for rectifier drops and harmonic compensation. The paper also analyzes load-induced output-voltage instability using equivalent and structural circuit models of the converter, deriving expressions for dynamic output resistance between channels. It concludes that a common multiwinding choke can reduce converter size and weight while lowering filter resistance and thereby improving output-voltage stability.
Full Text
ON THE USE OF A COMMON SMOOTHING CHOKE IN A STABILIZED VOLTAGE CONVERTER
I. A. GONCHAR, V. I. STEPANOV
(Submitted by the scientific and technical seminar of the Department of Automation and Telemechanics)
Stabilized power supplies that convert the voltage of a storage battery into a series of DC voltages must, as a rule, satisfy the principal requirements: high efficiency, reliability, small dimensions, and low weight.
Consideration of various versions of voltage converters with several outputs has led to the conclusion that multichannel voltage converters constructed according to the diagram in Fig. 1 can most fully satisfy the stated requirements.
Fig. 1. Block diagram of a multichannel converter
The conversion of DC voltage into AC is carried out by an inverter, which consists of a master oscillator, a pulse-duration modulator, a power amplifier, and a transformer with several output windings. A rectifier and a smoothing filter are connected to each output of the transformer.
For stabilizing the output voltages of the multichannel converter, a single feedback circuit is used, whose signal...
is taken from an additional winding of the transformer and, after rectification, smoothing, and comparison with a reference voltage, is fed to the modulator. The inverter simultaneously performs the function of the regulating element, since the duration of the voltage pulses at the output of the power amplifier is proportional to the error signal (Fig. 2, a).
If the smoothing filters of each channel contain chokes, then, as studies show, they largely determine the dimensions and weight of the entire converter (especially when the number of channels is large).
The weight and dimensions of a multichannel voltage converter can be substantially reduced if the separate filter chokes are replaced by a single choke with several windings. In doing so, correspondence must be ensured between the direct currents and the alternating voltages in the windings of the common choke, i.e., proper phasing of the alternating voltages and of the numbers of turns in the choke windings.
The requirement of proper phasing of the alternating voltages presents no difficulty, since for this it is sufficient to maintain the same direction of currents in all choke windings. Figure 3 gives an example of the connection of the choke windings. The direction of current in all windings is taken from the beginning of the winding.
Fig. 2. Voltage and current diagrams
Ensuring correspondence of the numbers of turns in the choke windings is a serious problem. The smoothing properties of the entire choke depend on this. The literature [1] gives an approximate calculation of a common choke when supplied from an AC network. A certain inaccuracy in calculating the ratios of choke turns leads to insufficient smoothing of the output voltages. In addition, the inductances of the choke windings in a DC voltage converter must be matched to the operating mode of the converter transistors.
Fig. 3. Circuit diagram of the choke-winding connections
Figure 2, c shows the variation of the current in the choke windings. We shall take as the smoothing coefficient of the choke the ratio of the mean value of the current to the difference between the maximum and minimum currents.
\[ k_{\mathrm{dr}}=\frac{I_0}{i_{\max}-i_{\min}}. \]
For a transistor amplifier, usually operating in class D, it is desirable that \(k_{\mathrm{dr}}\) have the maximum value, in order to ensure uniform current flow through the transistors and to reduce losses due to their heating.
In this paper, calculations are proposed for the common choke and for the stability of the output voltages under changes of the loads in the channels; on the basis of the latter, the expediency of using a common choke is shown.
Calculation procedure
- We calculate the total power consumed by all channels from the transformer
\[ \Sigma P = \Sigma I_0 (U_0 + u_{\mathrm{d}}), \tag{2} \]
where
\[ \begin{aligned} I_0&\text{— maximum load current,}\\ U_0&\text{— voltage across the load,}\\ u_{\mathrm{d}}&\text{— voltage drop across the rectifier diodes.} \end{aligned} \]
- We calculate the magnitude of the electromagnetic energy of the choke. When the energy stored in the choke is sufficient for current to flow in the choke winding during the intervals between pulses, the condition
\[ 2 i_{\mathrm{n}} L > (U_0 + u_{\mathrm{d}})(1-\gamma)T \tag{3} \]
must be satisfied.
Hence, for the common choke, with full-wave rectification, we obtain
\[ L_{\mathrm{kr}} I_0^2 = \frac{\Sigma P(1-\gamma)}{4f}, \tag{4} \]
where
\[ \gamma\text{— minimum relative duration of the П-shaped pulses.} \]
\[ \gamma = \frac{t_{\mathrm{i}}}{T}, \]
\[ f\text{— converter frequency } f=\frac{1}{T}. \]
\[ L I_0^2 = k_{\mathrm{dr}}\cdot L_{\mathrm{kr}}\cdot I_0^2 . \tag{5} \]
The total load must not vary by more than a factor of \(k_{\mathrm{dr}}\). Otherwise \(k_{\mathrm{dr}}\) should be increased.
- Analogously to the method for calculating [2] a choke with a single winding:
a) determine the steel volume of the core \(V_{\mathrm{st.akt.}}\);
b) find the auxiliary quantity \(M\)
\[ M=\frac{L I_0^2}{V_{\mathrm{st.akt.}}}; \tag{6} \]
c) determine the relative value of the effective magnetic permeability \(\mu_{\mathrm{eff}}\) and the relative length of the optimum air gap \(l_z\%\);
d) choose the current density;
e) find the limits of permissible changes in the length of the basic linear dimension \(a\) of the magnetic core;
f) finally refine the standard size of the magnetic core;
g) determine the total nonmagnetic gap in the magnetic core.
- Determine the inductance of the first winding of the choke
\[ L_{1\mathrm{ob}}= \frac{(u_{01}+u_{\mathrm{d}})k_{\mathrm{dr}}(0.5-\gamma)} {4\cdot f\cdot \Sigma P}. \tag{7} \]
- We find the number of turns of this winding
\[ w_{1\mathrm{dr}}=10^{4}\sqrt{\frac{L_{1\mathrm{ob}}\cdot l_{\mathrm{st}}}{1.26\,\mu_{\mathrm{eff}}S_{\mathrm{st}}}}, \tag{8} \]
where \(S_{\mathrm{st}}\) is the cross section of the center limb, \(\mathrm{cm}^{2}\);
\(l_{\mathrm{st}}\) is the length of the mean magnetic path, \(\mathrm{cm}\).
- We find the number of turns of each choke winding from the ratio
\[ \frac{w_{1\mathrm{dr}}}{w_{1\mathrm{tr}}} = \frac{w_{2\mathrm{dr}}}{w_{2\mathrm{tr}}} = \frac{w_{3\mathrm{dr}}}{w_{3\mathrm{tr}}}\ldots, \tag{9} \]
where
\(w_{1\mathrm{tr}};\; w_{2\mathrm{tr}};\; w_{3\mathrm{tr}}\ldots\) are the numbers of turns of the transformer output windings that produce the supply voltage of the corresponding channel in one of the half-periods.
- We calculate the required total electrostatic energy of all capacitors.
When the active resistance of the choke windings is small and the ripple swing at the filter output is small, the relative ripple amplitude is equal to [3]
\[ \delta=\frac{\Delta U'_{\mathrm{out}}}{2U_{0}} = \frac{T^{2}(1-\gamma)}{16LC}. \]
For a full-wave rectifier circuit,
\[ \delta=\frac{(0.5-\gamma)}{64f^{2}LC}. \tag{10} \]
Hence the total electrostatic energy of the capacitors is
\[ W_{C}=\frac{(\Sigma P)^{2}(0.5-\gamma)}{128\,L\,U_{0}^{2}\,f^{2}\delta}. \tag{11} \]
- We distribute this electrostatic energy among all filter outputs in direct proportion to the output powers and calculate the capacitance of the capacitor at the output of each stage
\[ C_{n}=\frac{2\cdot W_{C}\cdot P_{n}}{U_{n}^{2}\Sigma P}, \tag{12} \]
where
\(C_{n};\; P_{n};\; U_{n}\) are, respectively, the capacitance of the capacitor, the power, and the voltage of the \(n\)-th channel.
With strong coupling between the windings, the relative magnitude of ripples and voltage jumps resulting from transient processes will be equalized. Thus, it is possible to reduce the capacitance in one channel somewhat and increase it in another, while preserving the total electrostatic energy of all capacitors. Partial smoothing of the ripples of one channel is obtained by a capacitor connected in another channel. This latter property of the common choke can be used to reduce the dimensions of capacitors when smoothing ripples in a low-voltage channel. It is known that low-voltage (on the order of 6 V) electrolytic capacitors have considerably less stored energy than high-voltage ones (on the order of 300–450 V) for the same dimensions.
Sometimes [1] the number of turns in each winding is calculated using the ratio of the output voltages of each channel. Since this ratio does not include the voltage drops across the rectifier sels, …
diodes, such a calculation leads to incomplete effectiveness of the common choke. This is especially noticeable at low output voltages.
The calculation of the number of turns of the choke based on the use of the ratio of the number of turns of the transformer is more accurate, because in this case the alternating component in the choke windings is proportional to the voltage in the transformer windings and compensates the harmonics arising during voltage rectification.
Effect of the Load on the Stability of the Converter Voltages
For multichannel voltage converters, analysis of the effect of a varying load on the output voltages of the individual channels is of definite interest.
When estimating the instability of a voltage converter caused by changes in the load currents of the individual channels, the output transformer of the inverter may be represented by the equivalent circuit shown in Fig. 4 [4].
Fig. 4. Equivalent circuit of a multiwinding transformer
Here \(Z_0, Z_1, Z_2, \ldots, Z_n\) are the equivalent resistances of the transformer, determined from short-circuit tests; \(Z_{n1}, Z_{n2}, \ldots, Z_{nn}\) are the equivalent load resistances of the corresponding channels; \(n\) is the number of channels of the voltage converter.
Analysis of the static operating mode of the voltage converter can be carried out using the structural diagram shown in Fig. 5. The following designations are adopted in this diagram:
\(\kappa_{Ti}\) \((i = 1, 2, \ldots, n)\) are the transformation coefficients for the individual windings of the inverter output transformer;
\(\kappa_{vi}, \kappa_{\phi i}\) are the static transfer coefficients of the rectifiers and filters of the individual channels;
\(R_{vi}, R_{\phi i}\) are the equivalent resistances of the rectifiers and filters of the individual channels;
\(\kappa_{y0}\) is the static transfer coefficient of the modulator–amplifier circuit;
\(\kappa_{oc}\) is the static transfer coefficient of the feedback circuit, which takes into account the transformation coefficient of the feedback winding, the transfer coefficients of the rectifier and of the feedback filter.
The influence of the load current of one channel on the voltages of other channels occurs owing to the voltage drop across the transformer resistance \(Z_0\).
After structural transformations, the diagram in Fig. 5 is reduced to the simpler form shown in Fig. 6. The resistances \(Z_{pi}\) \((i = 1, 2, \ldots, n)\) in this diagram are determined by the relation
\[ Z_{pi} = Z_i + \frac{R_{\phi i} + R_{vi}}{\kappa_{Ti}^{2} \cdot \kappa_{\phi i} \cdot \kappa_{vi}}, \tag{13} \]
and the transfer coefficients of the converter output circuits are
\[ \kappa_{pi} = \kappa_{Ti} \cdot \kappa_{vi} \cdot \kappa_{\phi i}. \tag{14} \]
The instability of the output voltage of the \(k\)-th channel, caused by a change in the load current in the \(i\)-th channel, is determined by the relation known from the literature [5]
\[ \Delta U_{\mathrm{nk}} = R_{\mathrm{out}\,ki}\,\Delta I_{\mathrm{ni}}, \tag{15} \]
Fig. 5. Structural diagram of the voltage converter
where
\(R_{\mathrm{out}\,ki}\) is the dynamic output resistance of the \(k\)-th converter channel with respect to the load current in the \(i\)-th channel.
Fig. 6. Simplified structural diagram of the voltage converter
\(\Delta I_{\mathrm{ni}}\) is the change in load current in the \(i\)-th channel.
The dynamic output resistances of the converter can be found from the following relations, obtained from the structural diagram of Fig. 6:
\[ \left. \begin{aligned} R_{\mathrm{out}\,ki} &= \frac{\Delta U_{\mathrm{nk}}}{\Delta I_{\mathrm{ni}}} = -\kappa_{\tau i}\, \frac{Z_0}{1+\kappa_{y0}\kappa_{\mathrm{oc}}}\, \kappa_{\rho k}, && \text{for } k \ne i,\\[6pt] R_{\mathrm{out}\,kk} &= \frac{\Delta U_{\mathrm{nk}}}{\Delta I_{\mathrm{nk}}} = -\kappa_{\tau k} \left( Z_{\rho k} + \frac{Z_0}{1+\kappa_{y0}\kappa_{\mathrm{oc}}} \right) \kappa_{\rho k}, && \text{for } k=i . \end{aligned} \right\} \tag{16} \]
The output-voltage instability, in percent, is finally found as
\[ \delta_{ki}=R_{\text{out }ki}\frac{\Delta I_{ni}}{U_{nk}}\,100\%, \tag{17} \]
where
\(U_{kn}\) is the nominal output voltage of the \(k\)-th channel.
As is evident from relations (16), the principal instability of the output voltage in each channel is caused by a change in the load current in that same channel. The influence of the currents of the other channels on the \(k\)-th voltage is weakened by the presence of feedback in the converter.
This circumstance is explained by the fact that the dynamic resistance \(R_{\text{out }kk}\) is almost entirely determined by its first component—the resistance of the open-loop part of the converter, \(Z_{pk}\), which includes the resistance of the smoothing-filter choke. Moreover, the latter is predominant in the resistance \(Z_{pk}\).
Therefore, reducing the active resistance of the smoothing-filter choke by using a multiwinding choke leads not only to a reduction in the dimensions and weight of the voltage converter, but also to an increase in the stability of its output voltages.
REFERENCES
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- I. I. Belopol’skii, L. G. Pikalova. Calculation of Transformers and Chokes of Low Power. Gosenergo, 1963.
- E. E. Belmer. Smoothing properties of an inductance-capacitance filter with rectangular output-voltage pulses. Avtomatika i telemekhanika, No. 3, 1968.
- G. N. Petrov. Electrical Machines. Part 1, Gosenergo, 1956.
- V. I. Karpov. Semiconductor Voltage Stabilizers. Gosenergo, 1963.