Resistor model

The Maxwell and Voigt models of the last two sections have been investigated in all sorts of combinations. For our purposes, it is sufficient that they provide us with a way of thinking about relaxation and creep experiments. Probably one of the reasons that the various combinations of springs and dash-pots have been so popular as a way of representing viscoelastic phenomena is the fact that simple and direct comparison is possible between mechanical and electrical networks, as shown in Table 3.3. In this parallel, the compliance of a spring is equivalent to the capacitance of a condenser and the viscosity of a dashpot is equivalent to the resistance of a resistor. The analogy is complete... 

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. 

The thermally produced noise voltage X(t) appearing across the terminals of a hot resistor is often modeled by assuming that the probability density function for X(t) is gaussian,... 

Figures 5.29a and 5.29b show the Bode and Nyquist plot for a resistor, Ro, connected in series with a resistor, Rt, and capacitor, Ci, connected in parallel. This is the simplest model which can be used for a metal-solid electrolyte interface. Note in figure 5.29b how the first intersect of the semicircle with the real axis gives Ro and how the second intersect gives Ro+Rj. Also note how the capacitance, Ct, can be computed from the frequency value, fm, at the top of the semicircle (summit frequency), via C l JifmR .

Hodgkin and Huxley [81] formulated a membrane model that accounts for K" ", Na" ", and ion leakage channels in squid giant axons [Fig. 22(a)]. The membrane resting potential for each ion species is treated like a battery and the degree to which the channel is open is modeled by a variable resistor. 

The pH (or pI) term of the Nemst equation contains the electrode slope factor as a linear temperature relationship. This means that a pH determination requires the instantaneous input, either manual or automatic, of the prevailing temperature value into the potentiometer. In the manual procedure the temperature compensation knob is previously set on the actual value. In the automatic procedure the adjustment is permanently achieved in direct connection with a temperature probe immersed in the solution close to the indicator electrode the probe usually consists of a Pt or Ni resistance thermometer or a thermistor normally based on an NTC resistor. An interesting development in 1980 was the Orion Model 611 pH meter, in which the pH electrode itself is used to sense the solution temperature (see below). 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

The conductive particles in the volume of electrode make a so-called chain structures. As it is seen from the model, the electrical circuit assumes interconnection of the active mass particles in the solid phase of the electrode, while the external collector consists of a long chain of resistors. 

The first model of porous space as a 2D lattice of interconnected pores with a variation of randomness and branchness was offered by Fatt [220], He used a network of resistors as an analog PS. Further, similar approaches were applied in a number of publications (see, e.g., Refs. [221-223]). Later Ksenjheck [224] used a 3D variant of such a model (simple cubic lattice with coordination number 6, formed from crossed cylindrical capillaries of different radii) for modeling MP with randomized psd. The plausible results were obtained in these works, but the quantitative consent with the experiment has not been achieved. 

A first description of the microhotplate in AHDL was developed, which calculates the power dissipated by the polysilicon heater as shown in Fig. 3.3 [89]. The calculated power serves as input for a look-up table with the measured values of the power dissipated by a normalized polysilicon resistor, which then provides the corresponding microhotplate temperature. The model extracts the microhotplate temperature from the table. This microhotplate temperature is subject to temporal delay... 

The coefficients of thermal resistance can either be measured for existing devices or be calculated with the thermal microhotplate model presented in Chap. 3. In analogy to resistor-heated membranes, the model can be used for evaluation and optimization of new designs. A combination of the presented transistor model equations with the lumped microhotplate model in Sect. 3.4 would allow to also derive an AHDL model for coupled-system simulations. 

EIS data is generally interpreted based on defining an appropriate equivalent circuit model that best fits the acquired data. The elements of the circuit model involve a specific arrangement of resistors, capacitors, and inductors that tacitly represent the physicochemical reality of the device under test. Under these circumstances the numerical value for chemical properties of the system can be extracted by fitting the data to the equivalent circuit model. Impedance measurements are typically described by one of two models ... 

Exner and Fiedler have proposed a modified inductive effect (MIE). The MIE model represents transmission through two or more paths by an expression analogous to Kirch-hoff s Law for the resistance of parallel resistors. 

Most of the devices used by PSpice can include temperature effects in the model. Most of the semiconductor models provided by Oread include temperature dependence. By default, the passive devices such as resistors, capacitors, and inductors do not include temperature dependence. To make these items include temperature effects, you will need to create models that include temperature effects. The temperature dependence of resistors is discussed in Section 4.G.I. In this section, we will show only how the I-V characteristic of a 1N5401 diode is affected by temperature. The D1N5401 diode model already includes temperature effects so we will not need to modify the model. We will use the standard resistor, which does not include temperature effects. We will continue with the circuit of Section 4.B ... 

PSpice has three ways to specify temperature dependence. Three model parameters named TCI, TC2, and TCE are available. TCI and TC2 may be used together. If you use TCE, then TCI and TC2 are ignored. Suppose we have a resistor with a resistance equal to Rval. If TCE is specified, then the resistance is ... 

There are two ways to specify the temperature coefficients. One way is to create a resistor model and specify TCI, TC2, or TCE. The second way is to specify numerical values for the TCI and TC2 attributes of a resistor in the circuit. We will look first at the resistor attributes. Place a resistor part (R) in a schematic ... 

The second method is a resistor model that specifies temperature dependence. Every resistor that uses the model will have the same temperature dependence. Thus, if you have a circuit with many resistors, all from the same manufacturer and all with the same temperature characteristics, the same model can be used to specify the temperature characteristics of all of the resistors. Models will be covered in more detail in Part 7. Here we will just discuss making a model for resistors that includes temperature dependence. 

To create a resistor model, place a part called Rbreak in your circuit ... 

This window is a text editor. The name of the model is Rbreak. The only parameter specified in the model is R= 1. R is a model parameter used to specify the value of the resistance. If the value of the resistor specified in the schematic is x, then the actual value of the resistor used for calculations is x R. Since R is set to 1, the value of resistance specified in the schematic is also the value used in calculations. We can delete the model parameter R=1 or we can leave it in the model. It will have no effect on the simulations. We will now add the temperature coefficients. 

To specify a resistor with an exponential temperature coefficient of 0.0007 we would modify the model as follows ... 

Notice that the model name Rexp is now displayed next to the resistor. Rbreak is referred to as a breakout part. Since breakout parts are specifically used to create models, the name of the model used by the part is displayed on the schematic. 

We will now create two more models. Click the LEFT mouse button on the resistor graphic + of R3 to select it. 

Both R2 and R5 use the same model. If we had 100 resistors, we would use this last method to make them all use the sanrie model. Thus we would have to create only a single model, and then change the model reference of each resistor. 

To get an idea of how these resistors change with temperature, we will plot their resistance from -25°C to 1 5 Create the circuit below. Resistors R2, R3, and R4 use the models we just created. R5 has been deleted. Rx is a regu resistor (get a part named R) that has no temperature dependence. 

The curves generated here are arbitrary because we just randomly picked the temperature coefficients. To accurately model your resistors, you would need to get a data sheet on the resistors you are using and find out if the temperature dependence is linear, quadratic, or exponential, and also find the correct coefficients. The coefficients used here were just for illustration. 

Our first simulation will not specify temperature coefficients for any of the resistors. This will make the resistors independent of temperature. The model for the 2N3906 includes temperature dependence and will be the only device in the circuit that varies with temperature. Both Hfe and VBe are functions of temperature, and these parameters will affect Iq. 

We will now add temperature dependence to the previous circuit. A typical 1% resistor has a linear temperature coefficient of 100 parts per million, or 100x1 O 6. We will create a resistor model with this temperature coefficient. First, we will replace all resistors in the above circuit with the Rbreak part ... 

We will now edit the Rbreak model and create a model with the specified temperature coefficient. Click on the graphic for one of the resistors to select it. It should tum pink, indicating that it has been selected. After a resistor is selected, select Edit and then PSpice Model from the menus ... 

We have named the model RlOOPPtTl and specified the value of TCI to be lOOu, or 100x1 O 6. We will use this model for all of the resistors. Select File and then Save to save the model, and then select File and then Exit to close the model editor. When you return to the schematic, the resistor model name should be changed to RlOOppm ... 

We will now run a linear temperature sweep from -25 to 125°C to see how this circuit is affected by temperature. For the first simulation only the BJT will have temperature dependence. We will use normal resistors (part name R), which are independent of temperature. Note that the Q2n3906 BJT model includes temperature dependence. Set up the DC Sweep as shown ... 

We will create a resistor model with a 100 parts per million temperature coefficient. This model will be used by all resistors in the circuit ... 

SDLUTI0I1 Edit the resistor model to create a model with temperature dependence ... 

---