Circuit elements resistors

Time-resolved measurements on linear systems may be represented in many ways. For example, in the Nyquist representation, the transfer function H m) is plotted as a point in a two-dimensional plane having coordinates [Re(//) and Im(//)j, for each frequency measured. In specific cases, the transfer function may be represented also by an equivalent electrical circuit. This is a combination of lumped circuit elements (resistor, capacitor, etc.) having the same perturbation-response behavior as the system studied. 

Noise produced in passive circuit elements (resistors especially) is usually of thermal origin and has the mean-square voltage value... 

Even the tight controls in siUcon integrated circuit manufacturing are not yet sufficient to produce absolutely identical sensors on a single wafer. Cahbration of the final product is usually necessary, often by adjusting the value of a circuit element on the IC such as a resistor. The caUbration process can be automated, but it stiU adds to the cost of batch-fabricated sensors. Clever means of self-caUbration, particularly in field use, are constantiy being sought. 

In maldug electrochemical impedance measurements, one vec tor is examined, using the others as the frame of reference. The voltage vector is divided by the current vec tor, as in Ohm s law. Electrochemical impedance measures the impedance of an electrochemical system and then mathematically models the response using simple circuit elements such as resistors, capacitors, and inductors. In some cases, the circuit elements are used to yield information about the kinetics of the corrosion process. 

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. 

It should also be mentioned that capacitors were then added in parallel with the resistors in equivalent circuit elements because the frequency-dependent experimental electrical impedance data had a component that was 90° out of phase with the resistor. 

Notice that dashed lines associate a number with a circuit element. Note that the power numbers displayed for resistors are all positive. This means that those elements are absorbing that amount of power. The number displayed for the voltage source is negative, indicating that the element is sourcing power to the circuit. 

If we make a subcircuit out of this circuit, we could run into problems when the circuit is used. A problem that may result is that, if any of the terminals are not connected to other circuit elements, PSpice may generate an error message that only one element is connected to a certain node. To avoid this problem, we will add resistors to the circuit that do not affect its operation ... 

The resistors have a value of IT or 1012 2. These resistors are so large that they will not affect the operation of the circuit in most cases, and they avoid the problem of only one circuit element being connected to each node. 

Figure 2 The calculated potential distribution across a DSSC modeled by the resistor network of Fig. 1. The node number corresponds to distance through the cell in this case, the cell was modeled with 100 circuit elements. See the text for details.

Electrical diagrams contain symbols used to represent the various circuit elements. For example, Figure 10.5 is a simple DC circuit containing a battery, a switch, and a resistor. 

The mathematical expressions which describe the impedance of some passive circuits are shown below, where a passive circuit is one that does not generate current or potential [129], In this regard, the impedance response of simple passive circuit elements, such as a pure resistor with resistance R, a pure capacitor with capacitance C, and a pure inductor with inductance L, are given, respectively ... 

Fig. 11.1. The transmission line circuit used to model these data. The left hand end of the transmission line is at the electrode/film interface. The right hand end is at film/electrolyte interface. The extended resistances, RP and Rx, correspond to the resistance to motion of electrons between trimer centres and ions through the pores respectively, (a) The potential in the central line of the diagram is the potential within the film, and the connecting capacitors modify this potential to produce the driving potentials to drive current through the resistors. The CR kinetic circuit elements for the interfacial process can be seen at each end of the transmission line, (b) The modified circuit when the capacitance, C in equation (9) is not negligible. The potential at the trimer and in the pores is given by E and E ...

Circuit elements can be classified into two categories, passive elements and active elements. The former consumes energy and the latter generates energy. Examples of passive elements are resistors (measured in ohms), capacitors (measured in farads), and inductors (measured in henries). The two typical active elements are the current source (measured in amperes), such as generators, and the voltage source (measured in volts), such as batteries. 

The technique that measures the AC impedance of a circuit element or an electric circuit is called AC impedance spectroscopy. As described in Section 2.4, the impedances of a resistor (X, ). a capacitor (Zc), and an inductor (ZL) for a sinusoidal system can be expressed, respectively, as follows ... 

The constant phase element (CPE) is a non-intuitive circuit element that was discovered in the course of investigations into responses from real systems. In general, a Nyquist plot (also called a Cole-Cole plot or complex impedance plane plot) should be a semicircle with the centre on the x-axis. However, the observed plot for some real systems was indeed the arc of a circle but with the centre located somewhere below the x-axis. Figure 4.1 shows the impedance spectra of a circuit of a resistor and a constant phase element connected in parallel. The centre of the semicircle is located at (l-n)x90° below the real axis. 

In Chapter 2, we presented different combinations of electrical elements (resistor, capacitor, and conductor). In this chapter we now present several typical circuits for electrochemical systems, along with their corresponding impedance calculations. 

Ohm s law. V = IR, where /is the potential across a circuit element, / is the current through it, and R is its resistance. This is not a generally applicable definition of resistance. It is only applicable to ohmic resistors, those whose resistance R is constant over the range of interest and V obeys a strictly linear relation to /. 

Fig. 104. Equivalent circuits for the analysis of photocurrent-decay transients. The circuit elements are C, photocapacitor Rseries, total series resistance of the spectroelectrochemical cell Rl, load resistor Rin, internal leakage resistor R0, C , resistor and capacitor of counterelectrode solution interface Rd, resistance due to damaged surface layer.

The rapid development of solid-state electronic devices in the last two decades has had a profound effect on measurement capabilities in chemistry and other scientific fields. In this chapter we consider some of the physical aspects of the construction and function of electronic components such as resistors, capacitors, inductors, diodes, and transistors. The integration of these into small operational amplifier circuits is discussed, and various measurement applications are described. The use of these circuit elements in analog-to-digital converters and digital multimeters is emphasized in this chapter, but modern integrated circuits (ICs) have also greatly improved the capabilities of oscilloscopes, frequency counters, and other electronic instruments discussed in Chapter XIX. Finally, the use of potentiometers and bridge circuits, employed in a number of experiments in this text, is covered in the present chapter. 

All silicon integrated circuits (SICs) begin life as a silicon wafer, which has been cut from a silicon ingot and polished on one side to provide a smooth surface upon which thousands, even millions, of circuit elements such as transistors, diodes, and resistors will be fabricated and interconnected to yield a set of complete circuits. Circuit fabrication requires the selective difiusion of tiny amounts of impurities into specific regions of the silicon substrate to produce the desired electrical characteristics of the circuit. These regions are defined by lithographic processes that consist of two steps ... 

The term constant-phase element (CPE) is applied to a general circuit element that shows a constant phase angle. Thus, the resistor, capacitor, and inductor can all be considered to be constant-phase elements. 

Figure 4.5 Circuits demonstrating the calculation of the impedance of nested circuit elements a) circuit with resistor and capacitor elements b) reconstruction of the circuit in terms of the generic impedance Zj and c) secondary reconstruction to facilitate calculation.

The electrical circuits developed in Chapter 9 made use of boxes and undefined transfer hmctions Zy to account for the impedemce associated with interfacial reactions. In some cases, the interfacial impedance may be described in terms of such circuit elements as resistors and capacitors, but the nature of the impedance response depends on the proposed reaction mechanism. The objective of this chapter is to explore the relationship between proposed reaction mechanisms and the interfacial impedance response. 

In monolithic Integrated circuit technology, all circuit elements are fabricated on, or within, a single crystal piece of semiconductor material by means of a sequential series of diffusion, photolithography and thin film processes. As a production method, generally where thin film resistors are required, the following process sequence Is defined ... 

To prevent integrated circuit element breakdown, we incorporate protection resistors of NiFe film, the same material as the magnetic sensing element, in VB and Vout terminals and use a chip capacitor. The output signals of the peak and... 

Let us now reconsider the circuit element given by Fig. 3.29 and replace the input resistor by three parallel resistors, as shown in Fig. 3.30. Again, Kirchoff s law applied to the input of the amplifier in the light of property (3), and rearranged by Ohm s law and property (2), gives... 

Naturally, electrical engineers have designed equivalent circuits for nonelectrical wave phenomena. The waves may or may not be confined to cables. For simple propagating waves, the equivalent circuits are often called transmission line models. The transmission line has two ports representing input and output. The input-output relation can be predicted by applying the Kirchhoff laws to the set of elements located in between. The circuit elements may be simple resistors or capacitors, but their electrical impedance may also be a more complicated function of frequency (see, for instance. Fig. 6)... 

In the vicinity of resonances, the somewhat complicated algebraic form of the circuit elements can be approximated in such a way that they can be represented by resistors, capacitors, and inductances. If this is the case, one can intuitively understand the circuit. The famous Butterworth-van Dyke (BvD) circuit [66] (Fig. 7) can be derived from the Mason circuit. While the general form of the BvD circuit can be guessed without going back to the Mason circuit, the values of its elements can only be determined by the full derivation (Appendix A). 

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