On the waveform viewer and selecting Add Traces. Op amp-based circuit, then we add a new waveform. We want to see the gain and phase difference between our ideal equation and the In LTspice, it is possible to enter your own equations into the waveform viewer. LT6015 being 3.2 MHz, and the circuit in Figure 9 having a gain of -10 V/V. This follows from the gain bandwidth of the In Figure 9, at about 320 kHz the gain has rolled off from the ideal by 3 dB and In a simple scaling of the input voltage and a phase shift of 180°.
As a first example, let’s look at an inverting Comparing the Ideal to Modeled Implementationīy using LTspice to model a transfer function, you can take advantage of the Frequency and phase response of poles and zeros, all at 1 kHz.
Implementation of poles and zeros.įigure 8. The example file is PoleZeroExamples.asc. Its gain increases with frequency, reaching 0 dB gain at frequency ω z0.įigure 7 shows an example with these various poles and zeros implemented The leading “s” term is now referred to as a zero at the origin. If instead the example transfer function were written as: A pole results in a phaseĭelay of 90° and a decrease in gain around its frequency. Of 90° and an increase of gain around its frequency. Magnitude (that is, absolute value) of these roots. Note that the pole/zero frequencies are given by the The ω p0 term refers to the frequency at which the gain, due to the origin pole,įinding the roots of the numerator and denominator gives us the zero and poleįrequencies, respectively. Origin poles result in a constant phase delay of 90° and a gain response of –20 dB perĭecade. High gain at low frequencies, which eliminates steady state error in a control system. An origin pole is synonymous with an integrator and is used to provide extremely A Refresher on Poles and ZerosĪn example transfer function is given in Equation 3.ĭissecting Equation 3, we first see the term ω p0/s. Taking advantage of a text editor’s syntax highlighting. In the text editor, and then copy it into the LTspice dialog box. A simple RC circuit and its equivalent Laplace transform.Īs the transfer functions become larger, I have found it useful to use a codeĮditor, which automatically highlights matching parenthesis. Simulation, 2 we see that the two outputs match.įigure 5. The equivalent transfer function written using the Laplace transform. The Figure 5 simulation shows the step response of an RC impedance divider, and Spice command to cycle through some values. In Figure 4, are placed in curly brackets so that we can use the. In the Value field, enter “Laplace = ” followed by your equation, which shouldįigure 4. Right click the voltage source element to open its Component Attribute Editor. Placing a voltage dependent voltage source. The dialog box for this is shown in Figure 3.įigure 3. To implement the Laplace transform in LTspice, first place a voltage dependent The example file is Simple_RC_vs_R_Divider.asc. The Laplace transform allows us to describe how the RC circuit changes both gainĪnd phase over frequency. (red trace) is the same amplitude as the resistor divider, the phase delay is notable. Writing the transfer function in this form allows us to talk in terms of poles and zeros. The resistor divider is simplyīut the RC circuit is described by the slightly more complex Equation 2: The RC circuit also introduces a delay.įigure 2 shows two different transfer functions. Both the resistor divider and RC circuit reduce the amplitude by half with f = 1 kHz. The basic idea of a transfer function diagram is shown in Figure 1.įigure 2. Mathematical tool that allows us to work with the gain, frequency, phase, and For our purposes, we can think of it as a There are many resources available that discuss both the mathematics and We want to know how its output amplitude and phase compare with the input overįrequency.
Resistor divider or the speed of a car when you step on the gas. The system could be the output voltage of a Transfer functions are used when we want to analyze how the output of a systemĬhanges depending on the input. Files are available to aid in the understanding and implementation Response to a modeled implementation, and provides several useful examplesĪlong the way. The implementation of a transfer function in LTspice ®, compares the ideal Of a transfer function involves the Laplace transform. Transfer functions are used in the design of electronic systems such asįilters, power supplies, and other control systems.