First-order transient circuits are described by a first order differential equation. First-order circuits contain a resistor and only one type of storage element, either an inductor or a capacitor, i. RL or RC circuits. Where, is the circuit response atand is the response at. Therefore, the smaller the value ofthe faster the circuit response is. Applying the equations above, the voltage responses across the capacitor and the resistor in Figure can be written as:.
Figure 4 — 1 A first order circuit and its responses. Each of these step function inputs generates an output. Thus the total output response is the summation of all the individual output. Figure 4 — 2 — Circuits with step voltage sources. Figure 4 — 3 — Circuits with square wave input.First Order Transient Circuit Analysis
Build and simulate the circuits in Figure 4 — 3 using any simulation software such as MultiSim or Multisim Live. Set the input voltage to with a frequency of 1 kHz.
Display on the oscilloscope. Complete the measurements described below. Refer to Experiment 2 for how to use function generator and oscilloscope. On the oscilloscope, connect Ch1 to the input and Ch2 to the output so that both the input and the output are displayed on the screen. Save the screen image for both the input and the output, preferably to a USB drive.
Skip to content. Objectives To study the step response of first order circuits. To understand the concept of the time constant. Equipment Breadboard Function generator Oscilloscope Digital multimeter DMM Background First-order transient circuits are described by a first order differential equation.
Sketch or plot for each circuit. Square wave input For the circuits in Figure 4 — 3 use a square wave input. Assume that is a symmetric square wave with amplitude and period. Sketch or plot for each circuit using superposition. Show at least five cycles. Figure 4 — 2 — Circuits with step voltage sources Figure 4 — 3 — Circuits with square wave input Simulation Build and simulate the circuits in Figure 4 — 3 using any simulation software such as MultiSim or Multisim Live. Square wave output On the oscilloscope, connect Ch1 to the input and Ch2 to the output so that both the input and the output are displayed on the screen.
Time constant measurement Turn off the input Channel 1 by pressing the channel number button. Now only the output is displayed on the screen. Consider the rise and drop over one half cycle only for each circuit. Use cursors to determine the maximum voltage difference E for the output. Record this time constant for each circuit.Resonant circuits form the basis for filters that have better performance than first order RL, RC filters in passing desired signal or rejecting undesired signals that are relatively close in frequency.
The resonance frequency is defined as the frequency at which the impedance of the circuit is purely real, that is, with zero reactance.
For the reactance to be zero, impedance of the inductor must equal that of the capacitor. At resonance, the impedance of a branch with LC in series is equal to zero, which is equivalent to a short, and the admittance of a branch with LC in parallel is equal to zero, which is equivalent to an open.
As the frequency increases, the magnitude of an inductive reactance increases, while the magnitude of a capacitive reactance decreases. A circuit is said to be inductive if the total reactance is positive, and a circuit is said to be capacitive if the total reactance is negative. A bandpass, RLC circuit, will have two cut-off frequencies and where the amplitude is of the maximum value. The cut-off frequency is also called the half-power frequency or 3-dB frequency in some cases.
The bandwidth BW or passband bandwidth is defined as the difference between the upper and lower cutoff frequencies.
Circuit Theory/First Order Circuits
In case of a low-pass filter or baseband signal, the bandwidth is equal to its upper cutoff frequency. Examples of the resonance frequency, cutoff frequencies and the bandwidth are shown in Figure 8 — 1 for a bandpass and a bandreject filter. Figure 8 — 1 Resonance frequency, cutoff frequency, and bandwidth. The quality factor or Q factor of the frequency response is described quantitatively in terms of the ratio of the resonance frequency to the bandwidth.
This definition lends itself to laboratory measurement because it is possible to measure both the resonance frequency and the bandwidth. The Q factor is also defined as an energy ratio. The steady-state response of a circuit will in general have a maximum amplitude and phase angle that is different from that of the source. In some cases, the magnitude of the voltage response may exceed that of the voltage source. Skip to content. Objectives To study the behavior of series and parallel LC circuits at resonance.
To understand the resonance frequency, cut-off frequency, bandwidth and quality factor of a resonance circuit. To determine if a circuit is inductive or capacitive. To understand the circuit behavior at resonance. Equipment Breadboard Function generator Oscilloscope Digital multimeter DMM Background Resonant circuits form the basis for filters that have better performance than first order RL, RC filters in passing desired signal or rejecting undesired signals that are relatively close in frequency.
Preparation A. Derive the transfer function. Find the resonance frequency, cutoff frequencies, bandwidth and Q factor for each circuit. What is the phase relation between the total voltage and current, is it leading or lagging when the frequency is i below resonance, and ii above resonance?
What is the nature of the circuit in those two regions, ie, is it capacitive or inductive?
Explain your result.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. If your RC series circuit has a capacitor connected with a network of resistors rather than a single resistor, you can use the same approach to analyze the circuit.
The simple RC series circuit shown here is driven by a voltage source. Because the resistor and capacitor are connected in series, they must have the same current i t.
Generating current through a capacitor takes a changing voltage. Zero current implies infinite resistance for constant voltage across the capacitor. This gives you the voltage across the resistor, v R t :. You now have a first-order differential equation where the unknown function is the capacitor voltage. Knowing the voltage across the capacitor gives you the electrical energy stored in a capacitor.
In general, the capacitor voltage is referred to as a state variable because the capacitor voltage describes the state or behavior of the circuit at any time. A circuit reduced to having a single equivalent capacitance and a single equivalent resistance is also a first-order circuit.
The circuit has an applied input voltage v T t. To find the total response of an RC series circuit, you need to find the zero-input response and the zero-state response and then add them together.
Here is an RC series circuit broken up into two circuits. The top-right diagram shows the zero-input response, which you get by setting the input to 0. The bottom-right diagram shows the zero-state response, which you get by setting the initial conditions to 0. John M. Santiago Jr. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. About the Book Author John M.ECE Circuit Analysis. Fall version 8 October Damon A.
Course Format Summary This is only a summary; details are provided within this document. Miller will meet in-person with the class for two exam reviews as noted in the schedule. Students will be assigned one of three review sessions for each exam. Exams will be conducted during the scheduled lecture time. A link was emailed to the class. Help for at-home labs is available via lab instructor office hours. Note This syllabus provides a detailed course schedule from which supplemental materials e.
Office Hours Dr. Note that you may be online with other students; discussions related to confidential issues are by appointment as requested by email to damon. Laboratory Instructors. M PMPM. T AMAM. T PMPM. W PMPM. R AMAM. R PMPM. R 4PM-6PM. Catalog Description. ECE Circuit Analysis4 hrs. Analysis of linear electric circuits using methods based on Kirchhoff's laws and network theorems. Sinusoidal steady state analysis.
ECE faculty, including S. Durbin, J. GesinkJ. Kelemen, and F. Severance, contributed to course materials. Miller thanks current and past laboratory instructors that have contributed improvements to this course. He also thanks Instructional Designer M.First order circuits are circuits that contain only one energy storage element capacitor or inductorand that can, therefore, be described using only a first order differential equation.
The two possible types of first-order circuits are:. RL and RC circuits is a term we will be using to describe a circuit that has either a resistors and inductors RLor b resistors and capacitors RC. These can be arranged in parallel, or in series. Inductors are best solved by considering the current flowing through the inductor. Therefore, we will combine the resistive element and the source into a Norton Source Circuit.
The Inductor then, will be the external load to the circuit. We remember the equation for the inductor:. Wikipedia has related information at RL circuit. If we apply KCL on the node that forms the positive terminal of the voltage source, we can solve to get the following differential equation:.
Wikipedia has related information at RC circuit. An RC circuit is a circuit that has both a resistor R and a capacitor C. Like the RL Circuit, we will combine the resistor and the source on one side of the circuit, and combine them into a thevenin source. Then if we apply KVL around the resulting loop, we get the following equation:. In general, from an engineering standpoint, we say that the system is at steady state Voltage or Current is almost at Ground Level after a time period of five Time Constants.
From Wikibooks, open books for an open world. There are 3 pending changes awaiting review.
The latest reviewed version was checked on 14 June Circuit Theory. An RL parallel circuit. A parallel RC Circuit. Category : Book:Circuit Theory. Namespaces Book Discussion. Views Read Latest draft Edit View history. Reading room Community portal Bulletin Board Help out!
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Analyze a Series RC Circuit Using a Differential Equation
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