The Output Filter

The output filter converts the rectified rectangular ac waveform into the dc output. Forward-mode converters have a two-pole L-C filter which produces the dc average of the rectified rectangular waveform. Boost-mode converters have a single-pole, capacitive input filter which produces a dc voltage which is the peak voltage of the rectified waveform. Both are reactive impedance filters and exliibit very little loss. 

Designing the output filter choke La) in a forward-mode converter is done first. This simple procedure can be seen in Section 3.5.5. A key design factor is to design the inductor to operate in the continuous current mode. The typical value of peak inductor current is 150 percent of the rated output current. The typical valley (minimum) current is about 50 percent of the rated output current. 

3(min) is the smallest estimated duty cycle at high input line and at light load (an estimate of 0.3 is good). rippie(pk-pk) is the desired peak-to-peak output ripple voltage (volts). 

Capacitor manufacturers have only begun to specify the use of their capacitors in high frequency switching power supplies. One must use care when reviewing capacitors for use in one s power supply. The ESR should be specified at a frequency greater than 1 kHz. 

To properly design the capacitance for the output stage, one should place enough capacitors in parallel so that each capacitor operates at about 70 to 80 percent of its maximum ripple current rating. The sum of the capacitors should equal the final calculated value, but each capacitor should have the value of Ctot/fi, where n is the number of capacitors in parallel. 

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There are two basie types of output stage those used in forward-mode eon-verters and those used in boost-mode eonverters. The differenee is the presenee of the output filter induetor between the reetifier and the output filter eapaei-tor in the forward-mode output stage. Figure 3-28 shows the eommon output stages. 

This capacitor experiences the same current waveform at the power switch, which is a trapezoid with an initial current of about 1A rising to 2.8 A with very sharp edges. This capacitor has much more rigorous operating conditions than the output filter capacitor. I will estimate the RMS value of the trapezoidal current waveform as a piecewise superposition of two waveforms, a rectangular 1A peak waveform and a triangular waveform with a 1.8 A peak. This yields an estimated RMS value of 1.1 A. The value of the capacitor is then calculated as ... 

The output filter pole is determined by the filter induetor and eapaeitor and is a -40dB/deeade rolloff. Its nominal eorner frequency is... 

The values for the output filter capacitors are to be determined by using Equation 3.36. 

Designing the output-filter section (refer to Section 3.6)... 

Assign die approximate loeadon of the zero eaused by the ESR of the output filter eapaeitor at 20 KHz. 

The loeation of the lowest manifestation of the output filter pole oeeurs at the lightest antieipated output load on the power supply. The equivalent lightload resistanee is 28 V/f A or 28 ohms. It is found from... 

The zero in the eontrol-to-output eharaeteristie eaused by the ESR of the output filter eapaeitor ean be found by two methods if the value of the aetual ESR is known from the eapaeitor s data sheet, then the loeation of the zero ean be ealeulated, if not, it ean be grossly estimated. Using four aluminum eleetrolytie eapaeitors in parallel should eut the total ESR to one-quarter that exhibited by eaeh. I will estimate the zero to be at 10 KHz. 

Quasi-resonant converters utilize an T-C tank circuit, which rings at its natural resonance frequency in response to a step change in its terminal voltage or current. The tank circuit is placed between the power switch and the transformer and/or the transformer and the output filter. 

The zero eaused by the output filter eapaeitor(s) (ESR is two t50mohms in parallel) is... 

The form of compensation is the 2-pole-2-zero method of compensation. This is to compensate for the effect of the double pole caused by the output filter inductor and capacitor. One starts by determining the control-to-output characteristic of the open-loop system. 

Gdc = 20Tog(Ac) = +35dB The frequency of the output filter pole is... 

The next item is the zero exliibited by the series eombination of the ESR of the output filter eapaeitanee and the aetual value of the output filter eapaeitor itself. Its eorner frequency is found from... 

This causes the control-to-output characteristic to add gain and phase above the location of this zero. This can be a problem with respect to the stability of the supply. Unfortunately, many capacitor manufacturers do not present the value of the ESR for their capacitors. Typically, the zero caused by the output filter capacitor falls in the following range ... 

The output filter pole in both voltage-mode controlled flyback converter and the current-mode controlled forward and flyback is highly dependent on the equivalent resistance of the load. This means that when the load current increases or decreases, the location of the output filter pole moves. The filter pole can be found from... 

The zero attributed to the output filter capacitor is still present in the control-to-output characteristics. Its location is found in Section B.2.1 and Equation B.9. 

The location of the error amplifier s pole is used to counteract the effects of the output filter capacitor s zero caused by the ESR. The error amplifier s pole should be located by... 

The more complicated methods of compensation, such as this, allow the designer much more control over the final closed-loop bode response of the system. The poles and zeros can be located independently of one another. Once their frequencies are chosen, the corresponding component values can be easily determined by the step-by-step procedure below. The zero and pole pairs can be kept together in pairs, or can be separated. The high-frequency pole pair appear to yield better results if they are separated and placed as below. The zero pair are usually kept together, but can be separated and placed either side of the output filter pole s corner frequency to help minimize the gain effects of the Q of the T-C filter (refer to Figure B-23). 

Another major source of noise is the loop consisting of the output rectifiers, the output filter capacitor, and the transformer secondary windings. Once again, high-peak valued trapezoidal current waveforms flow between these components. The output Alter capacitor and rectifier also want to be located as physically close to the transformer as possible to minimize the radiated noise. This source also generates common-mode conducted noise mainly on the output lines of the power supply. 

The following equations are used to predict the pole and zero locations of the feedback loop. The output filter causes a double pole at... 

A zero is caused by the output filter capacitor, and the ESR of the outpi filter capacitor ... 

Because the ESR of the output filter capacitor creates a zero, it is essential to measure this term. The ESR measurement of output filter capacitor C6 is shown in Fig. 4.37. The ESR is approximately equal to 100 m 2 at the bandwidth of the converter. 

Now, in reality, the input impedance of the converter is frequency-dependent (Rin was just the low-frequency value of Zinput)- In the more detailed converter model, a parallel capacitance Qn (see Figure 13-3) appears across the input of the converter, mainly due to the output filter components of the converter being reflected into the input. This causes the (real part of the) input impedance to be less and less negative as frequency increases. 

Figure 1 Sketch illustrating principles of the standing cloud technique. Aerosol particles produced hy the nebulizer are captured by the output filter, direct analysis of drug or a marker of the drug such as a radiolabel provides a quantitative estimate of nebulizer function. (Modified from Ref. 7.)...

The output filter is designed to provide high gain and attention of high frequency noise. The transfer function is... 

In case the electronics in the feedback has frequency-independent response, the transfer function of the instrument would be proportional to acceleration. The output filter transfer function //out(ffl) is used to shape the low- and high-cutoff frequencies. 

A velocimeter is more common for broadband seismometers. In this case, an additional circuit, an integrator as a part of the output filter (//out(feedback amplifier (//fb(m) [Pg.952]

The main difference compared to the non-feedback case is that the adjusting procedure gives a much more accurate response of a seismometer within the passband than for the non-feedback sensor. Generally the high- and low-cutoff frequencies are extended by 2-3 octaves. In parallel with the feedback adjustment, a fine-timing of the output filter is done. In case the closed-loop response is actually flat over the passband, the device characteristics coincide with the output filter characteristics. This decreases the complexity of further device response presentation in terms of poles and zeroes. 

The last step in manufacmring the device is the adjustment of its sensitivity. The operation can be carried out by adjusting the overall gain of the output filter s //out(m). 

Mode 1 (Fig. 23(a)) During this mode, switches Q and Q2 of the HF inverter are on and the transformer primary current /pj and 1 2 is positive. The load current splits equally between the two cycloconverter modules. For the top cycloconverter module, the filter-inductor current (0.5 x / m) is positive and flows through the switches pair Sj and S(, the output filter Lf and Cf], switches S2 and 2, and the transformer secondary. Similarly, for the bottom cycloconverter module, the filter inductor current (0.5 /out) is positive and flows through the switches pair S5 and S5, the output filter Lj2 and Cj2, switches Sg and Sg, and the transformer secondary. 

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