:<math> i(t) = C \frac{dv}{dt} </math>
where v(t) and i(t) are the voltage and current of the capacitor, respectively, and C is it its capacitance. Similarly for an inductor, one can write:
:<math> v(t) = L \frac{di}{dt} </math>
== An Analog Differentiator Macromodel ==
A more practical voltage differentiator circuit using an ideal operational amplifier (Op Amp) is shown in the opposite figurebelow. The voltage transfer function of this circuit is given by:
:<math> \frac{ v_{out} }{ v_{in} } = - \frac{R_1}{1/sC_1} = -s \left( R_1C_1 \right) </math>
== An Analog Integrator Macromodel ==
[[Image:Integ1.png|thumb|400px|A practical voltage integrator circuit using an Op Amp.]]
A practical voltage integrator circuit using an ideal Op Amp is shown in the opposite figure. The voltage transfer function of this circuit is given by:
which represents a integral operator in the Laplace s-domain. This circuit is very similar to the Op Amp differentiator except for the fact that the timing resistor and capacitor have switched places.
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[[Image:Integ1.png|thumb|left|640px|A practical voltage integrator circuit using an Op Amp.]]
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An equivalent macromodel of the above circuit is given in the following figure, which represents RF.Spice's "Analog Integrator Block". In this model, the ideal Op Amp has been replaced with the linear controlled voltage source E2:
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[[RF.Spice]]'s "Generalized Analog Filter Block" does this realization automatically for any arbitrary filter order (or highest degree of the s-variable). You enter the denominator and numerator coefficients as arrays of real numbers. The figure below shows the property dialog of this black-box macromodel.
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You can access all these blocks from the '''Parts Menu'''. Some of the waveform generator devices are categorized as "voltage source" devices in the Device Manager's point of view. A number of the virtual blocks are native XSPICE models. You can find their models as "process models" in the Device Manager. Many others are "subscircuit models". You can open up, view and even modify their Netlist codes. Some other blocks like the generalized analog and digital filters do not have editable Netlist codes.
== A Note on the SPICE Simulation of Virtual Blocks ==
Most of the virtual blocks can be used in both transient and AC analysis tests. Obviously, nonlinear operations must be performed in the time domain. For example, you can see the performance of voltage controlled oscillators (VCO) only in a transient test, and using them in conjunction with AC frequency sweep analysis is meaningless. The same is true for frequency conversion blocks such as frequency multipliers. In addition, certain blocks such frequency conversion blocks may require harmonic wave input signals and may not work properly with arbitrary waveforms.