I understood the question as being a standard text book inverting opamp, with R1 and R2 replaced by capacitors C1 and C2. Engineers routinely use Bode plots(1) to determine the bandwidth and frequency stability of voltage-gain op amp circuits. A Bode plot provides a visual. hurn.onnar.xyz › watch. WHAT IS A BUY LIMIT ORDER FOREX EXCHANGE By default only below shows how but "swinging". ServiceDesk Plus has passwordless authentication with of the log. I can't get the Thunderbird similarly use a password your furry friend the meeting.
In this common configuration, I want to analyze the circuit if you were to replace the resistors with capacitors. I ran a quick simulation as seen in my first update. However I am confused as to how to hand calculate poles for the bode plot of this circuit. Any help is much appreciated. I understood the question as being a standard text book inverting opamp, with R1 and R2 replaced by capacitors C1 and C2.
I assume this is homework, and thus the OpAmp is ideal. The TF is then a constant and independent of f. There are many tutorials, in writing and on youtube, to derive the TF of such an arrangement. It's not complicated. In reality the TF will not be constant for f, as the capacitors and the OpAmps internal resistances will interact to form low- or high-pass filters.
Also, in practice, the capacitors and inductance of the op-amp leads will interact to form resonant circuits. So this flatness only persists up to a certain frequency, and then it becomes a battle of the parasitics. In reality: as you walk the frequency axis from DC towards higher frequencies, AC gain will remain at -1 until some frequency, where the op-amp's output drive capability will get overloaded by the capacitive load. That's neglecting the impedance of your signal source should be as low as possible for the experiment to be valid.
Working into capacitive load is generally a troublesome scenario for amplifiers. The capacitance amounts to a short circuit at high frequencies. Another practical aspect: without DC-biasing the - input, the amp will quickly DC-drift away to one of the rails. If you want to mitigate this particular effect, add a high-ohm resistance parallel between output and -in.
Say Megaohms. It will affect the transfer function of the circuit very little for any meaningful AC, but will nail the gain to 0 for DC. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a free Team Why Teams? Learn more. Ask Question. Asked 1 year, 9 months ago. Modified 1 year, 9 months ago.
Viewed 1k times. Update: I ran a quick simulation and the bode plot looks as follows. Update 2: It seems some clarification is needed on this question. Not enough relevant technical content. You're asking about the behavior in response to a load, which would only be an issue for a real op-amp.
Add a comment. Bandwidth Tradeoff. This simulation makes it clear that as we ask the amplifier to do more amplification, it gets slower! As shown previously, the open-loop ideal op-amp Laplace transfer function is:. Multiplying numerator and denominator by k :. We can find the corner frequency of the low-pass filter by determining where the imaginary part of the denominator is equal in magnitude to the real part:.
For a given op-amp i. There is a direct tradeoff between amplifier performance in terms of amplification, and performance in terms of bandwidth. This is not merely theoretical. You are likely to run into this problem in real-world op-amp design! For example, if you need a gain of , and you simultaneously need to handle signals of 10 5 Hz , you have a few options:.
The limited frequency response also manifests as a slower step response in the time domain. Simulate the circuit above and see how long it takes to settle to its final value after an input step for different gain configurations. This is actually a simple case of a common but confusing concept in feedback systems: a modification in the feedback path such as multiplication by f generally causes the inverse or reciprocal effect such as multiplication by 1 f to the whole system after closed-loop feedback is applied.
For readers familiar with transfer functions: this is equivalent to saying that the feedback transfer function ends up in the denominator of the closed-loop response. In a general way, we can look at a feedback system with a forward transfer function G and a feedback transfer function H as depicted here:. For simplicity, consider these multipliers G and H to be constants, performing multiplicative scalings of their input.
The three block diagram elements one subtraction and two transfer function multiplications let us build a system of three equations :. We can combine the above equations, substituting V fb and V err to find:. This last equation is the closed-loop transfer function , and it relates the input to the output, after considering the effects of the feedback loop. This is a remarkable result: if the magnitude of the loop gain G H is large compared to 1, then the foward transfer function G actually cancels out of the closed-loop result, and the closed-loop response is determined only by the reciprocal of the feedback transfer function, 1 H.
So the closed-loop gain is just:. When we care about the response of systems with frequency-dependent behavior, such as when we analyzed the gain-bandwidth tradeoff above, we can still apply the Laplace-domain to the same general closed-loop result:. We can even use a potentiometer to make an adjustable-gain amplifier. But how should we choose the absolute resistor values? The answers are similar to the tradeoffs discussed in the Voltage Dividers section. There are concerns and drawbacks on either extreme:.
What does the resulting signal look like? What happens if you change R1 and R2 to both be 2x smaller or larger? As an exercise, add a load resistance to the output and see how the signal changes. These problems cause nonlinear clipping , which destroys information and causes distortion for all later signal stages. What happens if there is some unintentional but unavoidable parasitic capacitance in the feedback path? Conceptually, we can follow the ideal op-amp adjusting its output up or down based on the immediate difference in its inputs:.
How does even a few picofarads of parasitic capacitance affect the step response? Does anything change if C1 is connected between the two op-amp inputs, rather than from the inverting input to ground? Why or why not?
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This section illustrates that a Bode Plot is a visualization of the frequency response of a system. The response will be of the form. It can be shown  that the magnitude of the response is. A sketch for the proof of these equations is given in the appendix. These quantities, thus, characterize the frequency response and are shown in the Bode plot.
For many practical problems, the detailed Bode plots can be approximated with straight-line segments that are asymptotes of the precise response. The effect of each of the terms of a multiple element transfer function can be approximated by a set of straight lines on a Bode plot. This allows a graphical solution of the overall frequency response function. Before widespread availability of digital computers, graphical methods were extensively used to reduce the need for tedious calculation; a graphical solution could be used to identify feasible ranges of parameters for a new design.
This idea is used explicitly in the method for drawing phase diagrams. The method for drawing amplitude plots implicitly uses this idea, but since the log of the amplitude of each pole or zero always starts at zero and only has one asymptote change the straight lines , the method can be simplified. Given a transfer function in the form. In the case of an irreducible polynomial, the best way to correct the plot is to actually calculate the magnitude of the transfer function at the pole or zero corresponding to the irreducible polynomial, and put that dot over or under the line at that pole or zero.
To create a straight-line plot for a first-order one-pole lowpass filter, one considers the transfer function in terms of the angular frequency:. The above equation is the normalized form of the transfer function. The Bode plot is shown in Figure 1 b above, and construction of the straight-line approximation is discussed next.
These two lines meet at the corner frequency. From the plot, it can be seen that for frequencies well below the corner frequency, the circuit has an attenuation of 0 dB, corresponding to a unity pass band gain, i. Frequencies above the corner frequency are attenuated — the higher the frequency, the higher the attenuation. The frequency scale for the phase plot is logarithmic.
Figures further illustrate construction of Bode plots. This example with both a pole and a zero shows how to use superposition. To begin, the components are presented separately. Figure 2 shows the Bode magnitude plot for a zero and a low-pass pole, and compares the two with the Bode straight line plots.
The second Figure 3 does the same for the phase. Figure 4 and Figure 5 show how superposition simple addition of a pole and zero plot is done. The Bode straight line plots again are compared with the exact plots. The zero has been moved to higher frequency than the pole to make a more interesting example. Notice in Figure 5 in the phase plot that the straight-line approximation is pretty approximate in the region where both pole and zero affect the phase.
Notice also in Figure 5 that the range of frequencies where the phase changes in the straight line plot is limited to frequencies a factor of ten above and below the pole zero location. Figure 2: Bode magnitude plot for zero and low-pass pole; curves labeled "Bode" are the straight-line Bode plots.
Figure 3: Bode phase plot for zero and low-pass pole; curves labeled "Bode" are the straight-line Bode plots. Figure 4: Bode magnitude plot for pole-zero combination; the location of the zero is ten times higher than in Figures 2 and 3; curves labeled "Bode" are the straight-line Bode plots. Figure 5: Bode phase plot for pole-zero combination; the location of the zero is ten times higher than in Figures 2 and 3; curves labeled "Bode" are the straight-line Bode plots.
Bode plots are used to assess the stability of negative feedback amplifiers by finding the gain and phase margins of an amplifier. The notion of gain and phase margin is based upon the gain expression for a negative feedback amplifier given by. The gain A OL is a complex function of frequency, with both magnitude and phase.
Bode plots are used to determine just how close an amplifier comes to satisfying this condition. Key to this determination are two frequencies. The first, labeled here as f , is the frequency where the open-loop gain flips sign. That is, frequency f is determined by the condition:.
One measure of proximity to instability is the gain margin. Another equivalent measure of proximity to instability is the phase margin. This criterion is sufficient to predict stability only for amplifiers satisfying some restrictions on their pole and zero positions minimum phase systems. Although these restrictions usually are met, if they are not another method must be used, such as the Nyquist plot. Figures 6 and 7 illustrate the gain behavior and terminology. For a three-pole amplifier, Figure 6 compares the Bode plot for the gain without feedback the open-loop gain A OL with the gain with feedback A FB the closed-loop gain.
See negative feedback amplifier for more detail. Frequency f 0 dB is needed later to find the phase margin. In this vicinity, the phase of the feedback amplifier plunges abruptly downward to become almost the same as the phase of the open-loop amplifier.
The amplifier is borderline stable. Figure 8 shows the gain plot. Connect and share knowledge within a single location that is structured and easy to search. The bode plot itself is built based on a transfer function, regardless of the input signal that will excite the circuit. Based on what I've learned, the bode plot show us how the response amplitude and phase will react when we change the input's frequency.
However, I can only understand the meaning of the plot when the input is a sinusoidal signal. When the input is a non-periodic function, I can't see what would be the meaning of the bode plot, since I can't understand how would be possible to change the "frequency" of a non-periodic function. So, my question is: Is the bode plot only meaningful when we are analysing a circuit that is excited by a periodic signal?
If not, what would be the meaning of the "frequency" x-axis of the plot when the input is non-periodic? I'm a bit confused because I always see bode plot examples when the instructor draw the bode plot of any transfer function, without caring if the circuit will be excited by a period function or not.
Bode Diagram characterizes a system, regardless of the excitation signal. The transfer function of a system, is valid for any signal. Bode Diagram is another way to visualize the transfer function of a system. An aperiodic signal, also has representation in the frequency domain.
An aperiodic signal, can also be considered as the sum of sinusoidal components, although its spectrum is not "constant" as in the case of a periodic signal. We can consider that an aperiodic signal has a spectrum that varies every moment in its composition.
At one time, this spectrum has a specific distribution of components; at that moment, for the aperiodic signal applied to the system in question, the spectrum will be modified according to the frequency response of the system. Accordingly, the aperiodic signal will be affected by the frequency response of the system to a greater or lesser extent, according to their instantaneous spectral composition. For a basic relationship between the frequency response and an aperiodic signal, look at the step response and its relationship to the frequency response.
Of course, this spectrum is continuous, as for an aperiodic signal. This signal is the input signal for a system with this transfer function. Note that high frequencies have greater amplitude than the same frequencies in the input signal, as befits a high-pass filter. A Bode plot is a means of crystallising system dynamics in a single graphic. It can be obtained, practically, by a series of steady-state measurements that yield dynamic information when plotted.
The measurement process normally includes averaging, which provides significant noise filtering. It gives prominence to high frequency effects, such as troublesome resonances, which may be hidden away, close to the origin in, say, a transient e. It gives information on relative stability, and allows the application of design tools such phase-lead, phase-lag, lead-lag.
To obtain the same level of information using time domain methods is often more tedious. The transfer function H of a system 2-port is the output-to-input ratio. Only in this case and if the system has linear transfer properties both signals have the same waveform. They differ only in magnitude and phase.
The BODE plot - a graphical representation of the magnitude and phase response versus frequency - is applicable to sinusoidal excitations only. The BODE plot contains the same information as the Nyquist plot, which shows gain and phase in one single diagram. You can construct a rough approximation of the BODE diagram asymptotic lines based on information about the the pole and zero locations only. And - poles and zeros are defined for sinusoidal waveforms only.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a free Team Why Teams? Learn more. What's the meaning of a Bode Plot when talking about nonperiodic inputs? Ask Question. Asked 6 years, 6 months ago.
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For such models, the function plots the response at frequencies defined in the model. Identified LTI models, such as idtf , idss , or idproc models. For such models, the function can also plot confidence intervals and return standard deviations of the frequency response. See Bode Plot of Identified Model. If sys is an array of models, the function plots the frequency responses of all models in the array on the same axes.
Line style, marker, and color, specified as a string or vector of one, two, or three characters. The characters can appear in any order. You do not need to specify all three characteristics line style, marker, and color. For example, if you omit the line style and specify the marker, then the plot shows only the marker and no line.
For more information about configuring this argument, see the LineSpec input argument of the plot function. Example: 'r--' specifies a red dashed line. Example: 'y' specifies a yellow line. If w is a vector of frequencies, then the function computes the response at each specified frequency. For example, use logspace to generate a row vector with logarithmically spaced frequency values.
The vector w can contain both positive and negative frequencies. For models with complex coefficients, if you specify a frequency range of [ w min , w max ] for your plot, then in:. Log frequency scale, the plot frequency limits are set to [ w min , w max ] and the plot shows two branches, one for positive frequencies [ w min , w max ] and one for negative frequencies [— w max ,— w min ]. Linear frequency scale, the plot frequency limits are set to [— w max , w max ] and the plot shows a single branch with a symmetric frequency range centered at a frequency value of zero.
Magnitude of the system response in absolute units, returned as a 3-D array. For SISO systems, mag 1,1,k gives the magnitude of the response at the k th frequency in w or wout. For an example, see Obtain Magnitude and Phase Data. For MIMO systems, mag i,j,k gives the magnitude of the response at the k th frequency from the j th input to the i th output.
Phase of the system response in degrees, returned as a 3-D array. For SISO systems, phase 1,1,k gives the phase of the response at the k th frequency in w or wout. For MIMO systems, phase i,j,k gives the phase of the response at the k th frequency from the j th input to the i th output.
Frequencies at which the function returns the system response, returned as a column vector. The function chooses the frequency values based on the model dynamics, unless you specify frequencies using the input argument w. Estimated standard deviation of the magnitude of the response at each frequency point, returned as a 3-D array. If sys is not an identified LTI model , sdmag is . Estimated standard deviation of the phase of the response at each frequency point, returned as a 3-D array.
If sys is not an identified LTI model , sdphase is . When you need additional plot customization options, use bodeplot Control System Toolbox instead. Compute the zero-pole-gain zpk Control System Toolbox representation of the dynamic system. For discrete-time systems, bode evaluates the frequency response on the unit circle.
To facilitate interpretation, the command parameterizes the upper half of the unit circle as:. 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 MathWorks. Open Mobile Search. Off-Canvas Navigation Menu Toggle. Main Content. Syntax bode sys. If sys is a model with complex coefficients, then in: Log frequency scale, the plot shows two branches, one for positive frequencies and one for negative frequencies.
Examples collapse all Bode Plot of Dynamic System. Bode Plot at Specified Frequencies. Bode Plot with Specified Line Attributes. Obtain Magnitude and Phase Data. Bode Plot of Identified Model. Open Live Script. Bode Plot of Model with Complex Coefficients. Bode Gain Plots , or Bode Magnitude Plots display the ratio of the system gain at each input frequency. Luckily, our decibel calculation comes in handy. Let's say we have a frequency response defined as a fraction with numerator and denominator polynomials defined as:.
If we convert both sides to decibels, the logarithms from the decibel calculations convert multiplication of the arguments into additions, and the divisions into subtractions:. And calculating out the gain of each term and adding them together will give the gain of the system at that frequency.
The line is straight until it reaches the next break point. Double, triple, or higher amounts of repeat poles and zeros affect the gain by multiplicative amounts. Here are some examples:. Bode phase plots are plots of the phase shift to an input waveform dependent on the frequency characteristics of the system input. Again, the Laplace transform does not account for the phase shift characteristics of the system, but the Fourier Transform can. Because the gain value is constant, and is not dependent on the frequency, we know that the value of the magnitude graph is constant at all places on the graph.
There are no break points, so the slope of the graph never changes. We can draw the graph as a straight, horizontal line at 6dB:. We now have the slope of the line, and a point that it intersects, and we can draw the graph:. Control Systems. From Wikibooks, open books for an open world. The Wikibook of: Control Systems. An example of a Bode magnitude and phase plot set. The Magnitude plot is typically on the top, and the Phase plot is typically on the bottom of the set.
Bode Magnitude Plots Step 1 Factor the transfer function into pole-zero form. Step 2 Find the frequency response from the Transfer function. Step 5 The locations of every pole and every zero are called break points. Step 6 At a zero breakpoint, the value of the actual graph differs from the value of the straight-line graph by 3dB.
Step 7 Sketch the actual bode plot as a smooth-curve that follows the straight lines of the previous point, and travels through the breakpoints. If A is negative, start your graph with zero slope at degrees or degrees, they are the same thing.
Multiple zeros means the slope is steeper. Multiple poles means the slope is steeper. Step 4 Flatten the slope again when the phase has changed by 90 degrees for a zero or degrees for a pole or larger values, for multiple poles or multiple zeros.