Inductor series resistance

For example, a real inductor has the basic property of inductance L, but it also has a certain non-zero dc resistance ( DCR ) term, mainly associated with the copper windings used. Similarly, any real capacitor has a capacitance C, but it also has a small equivalent series resistance ( ESR ). Each of these terms produces ohmic losses — that can all add up and become fairly significant. 

In the buck however, note that though the output diode needs to be positioned close to the IC/switch, the output capacitor is not critical (its current is smoothened by the inductor). If we place a ceramic capacitor in parallel to the output capacitor, it is only for the purpose of decreasing high-frequency noise and ripple at the output even further. But it is really not mandatory, and can cause severe loop instability, particularly with voltage mode control, especially if the effective series resistance (ESR) of the output capacitor section becomes too low (less than 100 inQ typically). 

Theoretical filter performance is based on the assumption that we are using ideal components. However, real-life inductors are always accompanied by some winding resistance (DCR) and some inter-winding capacitance. Similarly, real capacitors have an equivalent series resistance (ESR) and an equivalent series inductance (ESL). 

In subsequent simulation runs, resistor R Rc representing the equivalent series resistance of the capacitor is set to zero, the inductor resistance R Rl, however, is kept as its value affects the output voltage of the boost converter as well as the power... 

The circuit is assumed to consist of an ideal inductor and capacitor, that is, the inductor has no associated series resistance and the capacitor has no associated shunt leakage conductance. 

In the parallel configuration, the same potential difference occurs across each and every element with the total current being the algebraic sum of the current flowing through each individual circuit element. Table 2-35 summarizes the equivalent resistance, conductance, capacitance, and inductance of series-parallel configurations of resistors, capacitors, and inductors. 

The simple series RLC electrical circuit of Fig. 9.2 consists of a direct-current (DC) power source (here a 3-V battery), a relay, and three loads in series a resistor of resistance R, a capacitor of capacitance C, and an inductor of inductance L. Assume first a DC potential E = E0, in series with R, C, and L the capacitance stores charge, the inductance stores current, and the resistance dissipates some of the current into Joule13 heating. The arrow shows the direction of the current (which, thanks to Franklin s unfortunate assignment, is the direction of motion of positive holes—that is, the opposite of the flow of negative electrons) the relay across L avoids conceptual difficulties about an initial current through the inductor. The current is usually denoted by I (from the French word "intensite"). These three components (R, C, and L) will be explored in sequence. 

The a.c. impedance technique [33,34] is used to study the response of the specimen electrode to perturbations in potential. Electrochemical processes occur at finite rates and may thus be out of phase with the oscillating voltage. The frequency response of the electrode may then be represented by an equivalent electrical circuit consisting of capacitances, resistances, and inductors arranged in series and parallel. A simplified circuit is shown in Fig. 16 together with a Nyquist plot which expresses the impedance of the system as a vector quantity. The pattern of such plots indicates the type and magnitude of the components in the equivalent electrical network [35]. 

What about the current rating This is largely determined by the amount of heat dissipation the inductor can tolerate. But its thermal resistance (in degC/W) is not determined by the winding configuration, rather by the exposed area of the inductor, and other physical characteristics. Therefore, whether in series or in parallel configuration, we have to maintain the same total I2R loss. For example, suppose we call the current rating in parallel as Ip ,... 

The Z-source DC circuit breaker basically consists of a silicon controlled rectifier (SCR) and two crossed L-C series connections. In case there is no fault, the SCR is on and the capacitors are charged by the voltage source. In steady state, the capacitor currents are zero, the voltages across the inductor vanish and a constant current fiows through the series connection of inductors and load. Suppose that the resistances of the inductors can be neglected and that the load is the parallel connection of a load resistor Rl and a load capacitor Cl - Then steady-state values are ... 

For the case where the standard and unknown resistances are both real, the introduced error is equivalent to that of an inductor in series with the unknown. The pseudoinductance will, of course, appear in addition to any physical inductance introduced by the leads. 

The circuit shown in Fig. 1.16 is a bandpass filter. It has a physical inductor, that is, one that has a resistance in series with an ideal inductor. The inductor in a physical circuit will always have a resistance in series with an ideal inductor. The presence of the series resistor has the effect of moving the poles of H s) away from the j axis, thereby preventing the transfer function from exhibiting a perfect open circuit at resonance. 

The leakage inductance of both coils has been modeled by an inductor in series with the load, since the current in the coils also produces leakage flux. These inductances are labeled L p and Lj, respectively. Notice that the leakage inductance for the secondary side has been divided by the turns ratio n, squared because it was reflected to the primary side. Resistors labeled Rp and Rj have also been placed in series with the load to represent the resistance of the conductors used to wind the coils. Again, the secondary resistance has been divided by the square of the turns ratio, since it was reflected. 

More advanced modeling of the dynamic behavior of ESs employs an advanced equivalent series model (Figure 6.11) using inductor L, internal resistance R, and complex pore impedance Zp elements [9-11]. For more detailed modeling process, please see Reference 11. 

It is, of course, true that the streamer is not a lossless conductor. As the streamer grows, work is done to produce the streamer. In modeling the voltage and current, for example, it was found to be useful to represent the streamer as a resistor and inductor in series (Sazama and Kenyon, 1979). The resistance is necessary to account for the fact that work is being done on the liquid. The Kerr effect data shows that the voltage drop across the streamer is a small fraction (less than 10%) of the total potential difference between the electrodes. 

When the parameter B > 0, the closed form for the Faradaic impedance in Eq. 7-58 can be represented by an equivalent circuit composed of a parallel combination of the charge-transfer resistance R = 1/A, a series combination of resistance R = G/B, and an adsorption inductor L = ItB. The double-layer capacitance and the solution resistance can be added to complete the circuit (Figure 7-17A). There are two semicircles in the complex impedance plane— a high-frequency capacitive and a low-frequency inductive (Figure 7-17B) ... 

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