Documentation Help Center. The Simulink uses signal connections, which define how data flows from one block to another. The Simscape model uses physical connections, which permit a bidirectional flow of energy between components. Physical connections make it possible to add further stages to the RC circuit simply by using copy and paste.

The circuit is driven by a voltage square wave. A modified version of this example exists on your system. Do you want to open this version instead? Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.

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### Activity 1 Part (b): Frequency-Response Identification of a Resistor–Capacitor (RC) Circuit

The command "hold on" keeps the existing graph and adds the next one to it. The command "hold off" undoes the effect of "hold on". In the command "text", the first two numbers give the X and Y coordinate of where the test willo appear in the figure. The command "plot" can plot more than one function simultaneously.

In fact, in this example we could get away with only one plot command. For more information type help plot in matlab.

As an example consider the following function:. Suppose that you have the following expression F s and would like to find the coefficient of the corresponding polynomial:. One finds than the coefficient of the polynomial, using the " poly " command:. To find the coefficient of the coresonding polynomials, one first define the column vector of the roots:.

## Analyzing the Response of an RLC Circuit

The coefficients are then found from the poly command:. Using the Bode command when the transfer function is specified as a ratio of two polynomials. The resulting graph is shown below. In that case one can find the polynomial of the nominator and denomator first by using the poly function and the conv function. One first defines a column vector of the roots -s1, -s2, etc. In which "den" corresponds to the polynomial of the denominator.

Finally, one can plot the Bode Diagram:. An altnerative command to plot the magnitude and phase of a transfer function is:. Using the plot command when the transfer function is not specifed as a ratio of polynomials. We need to define the range of the indpendent variable w before plotting the fucntion H jw. The results is shown below.

As can be seen it is the same graph as the one obtained from the Bode command. One can then plot the output of the system for a given input signal x t. Lets apply two sinusoidial input signals x1 and x2 of frequency 50 Hz:and Hz, respectively. The the corresonding output sigals are called y1 and y2, respectively. Since the system filters out higher frequencies we expect that the output y2 is considerably smaller than y1.

We can plot the outputs of y1 and y2 using the lsim comment:. The matlab code for the filter and the input and output signals is as follows.

The graphs of the inputs x1 and x2 top graph and the outputs y1 and y2 bottom graph illustrates the effect of the filtering action. The step response y t of the system with the above transfer function is obtained by the command step.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute to sign up. I designed the circuit and obtained the desired outputs correctly. I mean changing the frequency should change the gain or not? I also plotted the bode diagram for both circuits. While you will see a difference between the two time domain plots higher frequency resulting in a lower output, as expected you will not between the two frequency domain plots.

You are not instructing Matlab to provide gain:phase at a particular frequency for the two frequency domain plots, you have essentially instructed Matlab to run a frequency sweep and resultant bode plot twice. The simplest solution to demonstrate a difference at different frequencies is to change the bode function call from. PLEASE note, this isn't really needed as you can just read off of the original bode plot the magnitude at Hz and 2kHz and see a difference.

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 5 years, 1 month ago. Active 5 years, 1 month ago. Viewed 3k times. Why do you think it is odd? See my updated response as it is a slight tweak on the bode command to help show this. Active Oldest Votes. As a result you will not see any difference between these two plots. It is a 1st order system. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog.

The Overflow How many jobs can be done at home?This tutorial contains many matlab scripts. You, as the user, are free to use all codes for your needs, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. Email Vladimir Dobrushkin.

Suppose that we wish to analyze how an electric current flows through a circuit. An RC circuit is a very simple circuit might contain a voltage source, a capacitor, and a resistor see Figure. A battery or generator is an example of a voltage source. The glowing red heating element in a toaster or an electric stove is an example of something that provides resistance in a circuit.

A capacitor stores an electrical charge and can be made by separating two metal plates with an insulating material. Capacitors are used to power the electronic flashes for cameras. Current, I tis the rate at which a charge flows through this circuit and is measured in amperes or amps A. We assign a direction to the current.

A current flowing in the opposite direction will be given negative values. The source voltage, E tis measured in volts V. Kirchhoff's Second Law tells us that the impressed voltage in a closed circuit is equal to the sum of the voltage drops in the rest of the circuit.

Thus, we need only compute the voltage drop across the resistor, E Rand the voltage drop across the capacitor, E C. According to Kirchhoff's Law, this is. We will now investigate how our circuit reacts under different voltage sources. For example, we might have a zero voltage source the capacitor could still hold a charge.

We could also have a constant nonzero source of voltage such as a battery or a fluctuating source of voltage such as a generator.

We might even have a series of pulses of voltage where the current is periodically turned on and off. We would like to be able to understand the solutions to the above differential equation for different voltage sources E t. If we view the differential equation as an expression for computing how fast current is flowing across the capacitor, we can analyze our circuit from a geometric point of view and can actually say a great deal about circuits without solving a differential equation.

Example : We consider a simplest case when there is no voltage source in the circuit. Although explicit formula is possibleto find, w postpone its derivation to chapter 6 when Laplace transform will be available. Energy is stored in the magnetic field generated by a current flowing through the inductor.

The induced emf opposes the flow of the current through it. RL circuit contains an inductor, which creates hysteresis and noise in the circuit.

Since inductors are large in size, the corresponding RL circuits are bulky and expensive. They are appropriate for filtering of high power signals because of low power dissipation. As currents flows into the circuit, it generates a magnetic field, that change in the magnetic field causes a change in the flux of the field concatenated to the circuit, this in turn, by the Faraday-Neumann-Lenz law generates a voltage in the circuit that is opposite to the voltage that is generating the magnetic field.

## Activity 1 Part (a): Time-Response Identification of a Resistor–Capacitor (RC) Circuit

Dobrushkin This tutorial contains many matlab scripts. The fundamental passive linear circuit elements are the resistor Rcapacitor C and inductor L or coil. These circuit elements can be combined to form an electrical circuit in four distinct ways: the RC circuit, the RL circuit, the LC circuit and the RLC circuit with the abbreviations indicating which components are used.

RC and RL are one of the most basics examples of electric circuits and yet they are very rich in content.The hardware and software needed for this experiment will also be the same as used previously. Specifically, the Arduino board will be used for generating the input to the circuit and for measuring the output of the ciruit. The input to the circuit will be generated from one of the board's Digital Outputsapplied across the resistor and capacitor in series.

The output of the circuit will be the voltage across the capacitor which will be read via one of the board's Analog Inputs. This data is then fed to Simulink for visualization and for comparison to our theoretical predictions. In the previous activity we examined the time response of an RC circuit. The purpose of this activity is rather to understand the frequency response of the same circuit. Specifically, we are going to experimentally construct the magnitude plot portion of the Bode plot for the RC circuit.

In this activity we will sweep through a range of frequencies, but we will employ square wave inputs rather than sine wave inputs. In this regard, the magnitude response that we generate won't exactly correspond to the standard definition of frequency response.

The reason we will employ square wave inputs is to build intuition regarding the meaning of the circuit's frequency response based on the understanding of the circuit's step response we gained in Activity 1a. The idea behind frequency response analysis is to examine how a system responds to sinusoidally varying inputs of different frequencies.

If we have a linear system, as we do in this case, then a sinusoidal input of a particular frequency will generate in steady-state a sinusoidal output of the same frequency.

RC circuit in Simscape

The output, however, may have a different amplitude than the input and the output may be phase shifted as compared to the input. This idea is demonstrated below. One can understand the above by considering that if our system is represented as the transfer functionthen the output is simply the product of the transfer function and the input. Therefore, the output can be separated via a partial fraction expansion into a component with the poles of the transfer function representing the system's natural response and a component with the poles of the input signal.

If the system is stable, then the natural response will die out resulting in a steady-state output that has the same form poles as the input signal. When we consider a system's frequency response, we are specifically interested in how the amplitude and phase of the steady-state output compare to the sinusoidal input.

One way to represent this amplitude magnitude data and this phase data is as a Bode plot. A Bode plot consists of two graphs, one being the magnitude of the response the ratio of the output amplitude to the input amplitude, versus frequency, and the other being the phase of the response versus frequency.This solution represents the voltage across a discharging capacitor. Now, to obtain the voltage across a charging capacitor, let us consider this figure that includes a voltage source.

The following examples illustrate the use of Matlab for solving problems related to RC circuits. Plot the voltage across the capacitor if R equals 5k ohm, 10k ohms and 20k ohms.

This just means that we are going to explore three time constants. The resulting plot is. From the resulting plot of our transient analysis, we see that if the time constant is small, it takes a shorter time for the capacitor to charge up the smaller the time constant the faster the circuit response.

In the same charging circuit above, the input voltage is now a rectangular pulse with an amplitude of 10 volts and a width of 0. The plots should start from 0s and end at 1s. We are going to develop a function that will return the voltage and corresponding time of the response. The input parameters are the voltage source vsthe resistor r and capacitor c. Now, we are going to call the function from our main code, like this.

We can see that the first circuit reaches the maximum voltage of the source. The second circuit started its discharge before reaching the maximum voltage.

Scilab Your own Website?Documentation Help Center. The product LC controls the bandpass frequency while RC controls how narrow the passing band is. The Bode plot is a convenient tool for investigating the bandpass characteristics of the RLC network. Use tf to specify the circuit's transfer function for the values.

However, the attenuation is only dB half a decade away from this frequency. To get a narrower passing band, try increasing values of R as follows:. The waves at 0. The long transient results from the poorly damped poles of the filters, which unfortunately are required for a narrow passing band:. To analyze other standard circuit configurations such as low-pass and high-pass RLC networks, click on the link below to launch an interactive GUI.

A modified version of this example exists on your system. Do you want to open this version instead? Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Search Support Support MathWorks.

Search MathWorks. Off-Canvas Navigation Menu Toggle. No, overwrite the modified version Yes. Select a Web Site Choose a web site to get translated content where available and see local events and offers.

Select web site.