John Santiago

When doing circuit analysis, you need to know some essential laws, electrical quantities, relationships, and theorems.Ohm’s law is a key device equation that relates current, voltage, and resistance. Using Kirchhoff’s laws, you can simplify a network of resistors using a single equivalent resistor. You can also do the same type of calculation to obtain the equivalent capacitance and inductance for a network of capacitors or inductors.

The unit step (Heavyside) function models the behavior of a switch (off/on). The unit step function can describe sudden changes in current or voltage in a circuit. The unit step function looks like, well, a step. Practical step functions occur daily, like each time you turn mobile devices, stereos, and lights on and off.

There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. You can use series and parallel RLC circuits to create band-pass and band-reject filters. An RLC circuit has a resistor, inductor, and capacitor connected in series or in parallel.You can get a transfer function for a band-pass filter with a parallel RLC circuit, like the one shown here.

Filter circuits (such as low-pass filters, high-pass filters, band-pass filters, and band-reject filters) shape the frequency content of signals by allowing only certain frequencies to pass through. You can describe these filters based on simple circuits. You find the sinusoidal steady-state output of the filter by evaluating the transfer function T(s) at s = jω.

With simple RC circuits, you can build first-order RC low-pass (LPF) and high-pass filters (HPF). These simple circuits can give you a foundational understanding of how filters work so you can build more-complex filters. First-order RC low-pass filter (LPF) Here's an RC series circuit — a circuit with a resistor and capacitor connected in series.

Using the Laplace transform as part of your circuit analysis provides you with a prediction of circuit response. Analyze the poles of the Laplace transform to get a general idea of output behavior. Real poles, for instance, indicate exponential output behavior.Follow these basic steps to analyze a circuit using Laplace techniques: Develop the differential equation in the time-domain using Kirchhoff’s laws and element equations.

A first-order RC series circuit has one resistor (or network of resistors) and one capacitor connected in series. First-order RC circuits can be analyzed using first-order differential equations. By analyzing a first-order circuit, you can understand its timing and delays. Here is an example of a first-order series RC circuit.

When timing is off in your computer, specific events don’t occur in the right order. But if you know the physics and i-v relationships of resistors and capacitors, you can create a circuit that detects pulses; then when a pulse is missing, the circuit can trigger an alarm notifying the user of a timing problem.

Here’s your chance to convert light into electricity using simple operational circuits. You can apply a similar approach to develop instruments that measure other physical variables in the environment, such as temperature and pressure. You use an input transducer to turn a physical variable into an electrical variable.