LTspice Tutorial

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Tuesday, 20-Sep-2011 07:00:39 EDT Pages created and updated by Terry Sturtevant Date Posted: June 9, 2011 LTspice Tutorial While LTspice is a Windows program, it runs on Linux under Wine as well. (LTspice is also called SwitcherCAD by its manufacturer, since they use it primarily for the design of switch mode power supplies (SMPS).) Note: Some of this was written using SwitcherCad III, and some was written using LTspice IV. The instructions should be the same. Opening LTspice I. Drawing the circuit Making Sure You Have a GND A. Getting the Parts B. Placing the Parts C. Connecting the Circuit D. Changing the Name of the Part E. Changing the Value of the Part F. Using Net Labels G. Adding your own SPICE Models or Subcircuits H. Saving I. Printing J. II. Simulation Before you do the simulation A. Choosing a simulation B. Graphing C. Adding/Deleting Traces D. Doing Math E. Labelling F. Finding Points (aka Using Cursors) G. Saving H. Printing I. III. Simulation Commands DC operating point A. Transient B. AC Analysis C. DC Sweep D. Noise E. Parametric F. Temperature G. Other types of analysis H. IV. Types of Sources Voltage Sources DC 1. PULSE 2. SINE 3. EXP 4. SFFM 5. PWL 6. A. V. LTspice Tutorial http://denethor.wlu.ca/ltspice/ 1 of 29 9/20/2011 4:27 PM

Transcript of LTspice Tutorial

Tuesday, 20-Sep-2011

07:00:39 EDT

Pages created and updated by Terry Sturtevant Date Posted: June 9, 2011

LTspice Tutorial

While LTspice is a Windows program, it runs on Linux under Wine as well. (LTspice is also called SwitcherCAD byits manufacturer, since they use it primarily for the design of switch mode power supplies (SMPS).)Note: Some of this was written using SwitcherCad III, and some was written using LTspice IV. Theinstructions should be the same.

Opening LTspiceI.

Drawing the circuitMaking Sure You Have a GNDA.Getting the PartsB.Placing the PartsC.Connecting the CircuitD.Changing the Name of the PartE.Changing the Value of the PartF.Using Net LabelsG.Adding your own SPICE Models or SubcircuitsH.SavingI.PrintingJ.

II.

SimulationBefore you do the simulationA.Choosing a simulationB.GraphingC.Adding/Deleting TracesD.Doing MathE.LabellingF.Finding Points (aka Using Cursors)G.SavingH.PrintingI.

III.

Simulation CommandsDC operating pointA.TransientB.AC AnalysisC.DC SweepD.NoiseE.ParametricF.TemperatureG.Other types of analysisH.

IV.

Types of SourcesVoltage Sources

DC1.PULSE2.SINE3.EXP4.SFFM5.PWL6.

A.V.

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PWL File7.Current SourcesB.

References and LinksVI.

Opening LTspice:Find LTspice on the C-Drive. Open LTspice IV (or SWCad III). The opening screen will looklike this:

I.

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.Begin a new circuit

from the file menu, or

click on the "New Schematic" icon. Now you will see this:

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.

Drawing the circuit:Adding a GND: This is very important. You cannot do any simulation on the circuit ifyou don't have a ground. To place a ground, you can

press the 'g' key, or

A.II.

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use the ground icon, , orget it from the 'Edit' menu.

If you aren't sure where to put it, place it near the bottom of the drawing.Getting the other Parts:

The next thing that you have to do is get some or all of the parts you need.This can be done by

clicking on the icon for a specific component;

(This is good for common components such as resistors, capacitors, etc.)

clicking on the 'component' button; , orpressing "F2"; orgoing to "Edit" and selecting "Component..."

Once this box is open, select a part that you want in your circuit. This can be done bytyping in the name or scrolling down the list until you find it.

Some common parts are:res - resistorcap - capacitorind - inductordiode - diodevoltage - any kind of power supply or battery

Anything in [ ] is a library, which contains many parts.To rotate parts so that they will fit in your circuit nicely, press "Ctrl+R" before placingthe part. If you want to reflect (or 'Mirror') the part, press "Ctrl+E".Upon selecting your parts, click where you want them placed (somewhere on the greypage with the dots). Don't worry about putting it in exactly the right place, it canalways be moved later.Each type of part can be placed multiple times in succession, and they will beautomatically numbered. when you want to stop placing a particular type of part,right-click or press 'Esc'.

B.

Placing the Parts:C.

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You should have most of the parts that you need at this point.Now, all you do is put them in the places that make the most sense (usually a

rectangle works well for simple circuits). To move parts, click on the 'move' icon, and then you may select parts and drag them where you want them.(When you have a part selected for a move, you can rotate or reflect it as well.)If you have any parts left over, just select them and press "Delete".

Connecting the Circuit:Now that your parts are arranged well, you'll have to attach them with wires.Go up to the tool bar and

select the "Draw Wire" button , or"F3" orgo to "Edit" and select "Draw Wire".

With the pencil looking pointer, click on one end of a part, when you move your mousearound, you should see crossed lines appear. Attach the other end of your wire to thenext part in the circuit.Repeat this until your circuit is completely wired.If you want to make a node (to make a wire go more then one place), clicksomewhere on the wire and then click to the part (or the other wire). Or you can gofrom the part to the wire. You should see a square block when 3 or more wiresconnect at a point.Holding down CTRL while drawing lines allows you to make diagonal connections inthe editor.To get rid of the pencil, right click.

D.

Changing the Name of the Part:You probably don't want to keep the names C1, C2 etc., especially if you didn't putthe parts in the most logical order. To change the name, right click on the presentname (C1, or R1 or whatever your part is), then a box will pop up (Enter NewReference Designator), where you can type in the name you want the part to have.

Please note that if you double click on the part or its value, no box will appear.

E.

Changing the Value of the Part:If you only want to change the value of the part (if you don't want all your resistors tobe 1K ohms), you can right click on the part, (not the name), and a box title by thepart name (such as "Resistor") will appear. The number of fields in the box will dependon the type of part it is. Type in the new value and press OK. Use u for micro as in uF= microFarad.

F.

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Using Net Labels:These are important if you want to user your own identifiers for points in the networkwhere you want to determine voltages rather than having to work with the nodenumbers that LTspice assigns.To add net labels,

press "F4", or

click on the "Label Net" icon , orselect "Edit/Label Net" from the menu.

When you do this, a window will pop up where you assign the label you want to usefor the net.

G.

Adding your own SPICE Models or Subcircuits

How to add a model to LTspice (SwitcherCad)

This assumes you want to add a new model for a new device similar to one in the existinglibrary. Here are three different methods.

Method 1: Modifiy Libraries

This method makes sense if you are working on your own computer, where you can updateyour own libraries and use them again.

H.

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Look under C:\Program Files\LTC\LTspiceIV(or C:\Program Files\LTC\SwCADIII )

1.

Go to the directory lib\cmp2.Look at the list of standard devices to figure out which kind you want, such as:

standard.bjtstandard.diostandard.jft...etc...

Each line in each of these files has a model for one device.

3.

Add a line with the .model line for your device to the end of the appropriate file usinga text editor.Note you may have to adapt the model line to match the pattern in the file.It should be pretty easy to figure out.

4.

Now when you open LTSpice, you should be able to pick the device you've added as thoughit was one of the existing models.

Method 2: Using an external library file

This will work well if you are using a computer where you can't edit the built-in library files,or where edits will not be saved, but where you may have several models in one file whichyou would like to be able to use in the future.

Save the file which contains the model you want to use in a directory where you havewrite access. (For example, I use c:\windows\temp.)

1.

Insert a SPICE directive from the edit menu,

by using the icon, or by typing 'S'.In the text box, type.lib path to your library fileso, for example.lib c:\windows\temp\myfile.sp3

2.

Change the name of the component in your schematic to match the exact name of themodel in the library file.

3.

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Now when you simulate, your new device model should be used.Note: you can use the .include directive instead of the .lib directive if you wish.

Method 3: Inserting the model directly into the drawing

This will work well if you are using a computer where you can't edit the built-in library files,or where edits will not be saved, and that there is only a single model you want to use.

Open file which contains the model you want to use, and copy the model into theclipboard.

1.

Insert a SPICE directive from the edit menu, by using the icon, or by typing 'S'.In the text box, paste the model from the clipboard.

2.

Change the name of the component in your schematic to match the exact name of themodel in the model line.

3.

Now when you simulate, your new device model should be used.Note: Because you now have the model saved as part of your schematic, this is completelyportable between computers.

How to add a subcircuit model to LTspice(SwitcherCad)Sometimes you need to add something which is more complicated than simply a model.In this case you can add add a subcircuit model for a device. You'll save a bit of time if thenew device at least looks similar to one in the existing library. Otherwise you may have todraw a new symbol. (Suppose the file that contains the model you want to use is called1N5338B.LIB and the model you want to use is a subcircuit called 1N5338B.)

Method 1: Modifiy Libraries

This method makes sense if you are working on your own computer, where you can updateyour own libraries and use them again.

Look under C:\Program Files\LTC\LTspiceIV(or C:\Program Files\LTC\SwCADIII )

1.

Put the file 1N5338B.LIB in the subdirectory lib\sub .2.Go to the directory lib\sym3.Find a component similar to what you want. That way you won't have to draw thesymbol from scratch. For instance, if I were adding a new zener diode, I see there's acomponent zener.asy.

4.

Copy zener.asy to 1N5338B.asy. (1N5338B will be the name of the new zenerdiode model I want to use.)

5.

Open 1N5338B.asy in a text editor, and make the following changes:change SYMATTR Prefix D to SYMATTR Prefix X(This says that the model we're using is a .subckt.)change SYMATTR Value D to SYMATTR Value 1N5338B(This says that the name that will show up on the schematic is 1N5338B.)add a line SYMATTR ModelFile 1N5338B.LIB(This says that the name of the file containing the subcircuit we're using is1N5338B.LIB.)add a line SYMATTR SpiceModel 1N5338B(This says that the name of the subcircuit we're using is 1N5338B. You can seethis by looking at the first line of the file:.SUBCKT 1n5338b 2 1This tells the name of the subcircuit and that it has two pins.)

6.

Now when you open LTSpice, you should be able to find the component you have added,and use it like any of the ones that are built-in .

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Method 2 and Method 3: Setup

This same procedure applies to both methods. These methods will be useful where you can'tedit the library files. This might happen if you are working on computers in public las, forinstance.

Hold down CTRL-M while right-clicking on the component to bring up the dialog.1.

Change the prefix of the device to "X" to indicate you are using a subcircuit, and editthe value of the device to match the subcircuit name exactly.

2.

After these steps, go on to either Method 2 or Method 3.

Method 2: Using an external library file

This will work well if you are using a computer where you can't edit the built-in library files,or where edits will not be saved, but where you may have several models in one file whichyou would like to be able to use in the future.

Save the file which contains the subcircuit you want to use in a directory where you1.

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have write access. (For example, I use c:\windows\temp.)Insert a SPICE directive from the edit menu,

by using the icon, or by typing 'S'.In the text box, type.lib path to your library fileso, for example.lib c:\windows\temp\myfile.sp3

2.

Method 3: Inserting the model directly into the drawing

This will work well if you are using a computer where you can't edit the built-in library files,or where edits will not be saved, and that there is only a single model you want to use.

Open file which contains the subcircuit you want to use, and copy the subcircuit intothe clipboard.

1.

Insert a SPICE directive from the edit menu, by using the icon, or by typing 'S'.In the text box, paste the subcircuit from the clipboard.

2.

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The subbcircuit itself may include model definitions, so you may have to includeseveral lines when you copy. If the library file is only for that one device, then you'llwant to copy and paste the entire file contents.

Saving:

To save the circuit, use the save button on the tool bar or any other method youwould normally use to save files.

I.

Printing:

To print, you may use the menu or the print icon as usual.

J.

Simulation:Before you do the simulation:

You have to have your circuit properly drawn and saved.There must not be any floating parts on your page (i.e. unattached devices).You should make sure that all parts have the values that you want.There are no extra wires.

A.III.

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It is essential that you have a ground in your circuit.Choosing a simulation:

Click on the Simulate button on the tool bar or use the "Simulate/Edit SimulationCmd" command.

Enable whatever type(s) of anlysis you want using the Edit Simulation Commandwindow. The last one you choose is the one which will be done when you simulate.

Click on the Simulate button on the tool bar or use the "Simulate/Run" command.It will check to make sure you don't have any errors. If you do have errors, correctthem.

B.

Graphing:Go to the "View" menu:

C.

Adding/Deleting Traces:

Use "Visible Traces" or on the toolbar to select all the traces you want.The add traces window allows you to choose varaious signals from the circuit, or tocreate mathematical expressions involving them.

D.

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To delete a trace, select its title on the graph and press "Delete".Doing Math:

In Visible Traces, there are functions that can be performed, these will add/subtract(or whatever you chose) the lines together.

Select the signal(s) that you wish to have displayed.There are many functions here that may or may not be useful. If you want to knowhow to use them, you can use LTspice's Help Menu.

E.

Labelling:

Click on Text Label on top tool bar.Type in what you want to write.Click OKYou can move this around by single clicking and dragging.

F.

Finding Points: (aka Using Cursors)Click on the name of the trace you want to look at and then a cursor window willappear, showing information about the point currently selected.

G.

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.Note that if you right click on the trace name, you can choose to show two cursors.This then allows automatic math to be done, such as to give the difference betweenthem in both dimensions.You can use the cursor keys to move back and forth through the data points.

Saving:To save your probe you need to go into the tools menu and click display, this will openup a menu which will allow you to name the probe file and choose where to save it.You can also open previously saved plots from here as well.

H.

Printing:

Select Print in Edit or on the toolbar .Print as usual.

I.

Simulation CommandsDC Operating Point

This is a simple, but incredibly useful analysis. It will not give you anything to plot,but it will indicate the DC voltages at all nodes and DC currents through all devices inthe circuit.

A.

TransientB.

IV.

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The transient analysis is probably the most important analysis you can run in LTspice,and it computes various values of your circuit over time. Two very importantparameters in the transient analysis are:

Stop Time.Time to Start Saving DataMaximum Timestep(various checkboxes....later)

The ratio of Stop Time: Maximum Timestep determines how many calculationsLTspice must make to plot a wave form. LTspice always defaults the start time to zeroseconds and going until it reaches the user defined final time. It is incrediblyimportant that you think about what timestep you should use before running thesimulation, if you make the timestep too small the probe screen will be cluttered withunnecessary points making it hard to read, and taking extreme amounts of time forLTspice to calculate. However, at the opposite side of that coin is the problem that ifyou set the timestep too high you might miss important phenomenon that areoccurring over very short periods of time in the circuit. Therefore play with step timeto see what works best for your circuit.

You can set a step ceiling which will limit the size of each interval, thus increasingcalculation speed. Another handy feature is the Fourier analysis, which allows you tospecify your fundamental frequency and the number of harmonics you wish to see onthe plot. LTspice defaults to the 9th harmonic unless you specify otherwise, but thisstill will allow you to decompose a square wave to see it's components with sufficientdetail.

AC AnalysisC.

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The AC analysis allows you to plot magnitude and/or phase versus frequency for differentinputs in your circuit.

Type of SweepIn the AC anlysis menu you have the choice of three types of analysis:

Linear,Octave andDecade.

These three choices describe the X-axis scaling which will be produced in probe. Forexample, if you choose decade then a sample of your X-axis might be 10Hz, 1kHz,100kHz, 10MHz, etc.... Therefore if you want to see how your circuit reacts over avery large range of frequencies choose the decade option.

You now have to specify at how many points you want LTspice to calculatefrequencies, and what the start and end frequency will be. That is, over what range offrequencies do you want to simulate your circuit.

Number of pointsStart FrequencyStop Frequency

DC SweepD.

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The DC sweep allows you to do various different sweeps of your circuit to see how itresponds to various conditions.For all the possible sweeps,

voltage,current

you need to specify a start value, an end value, and the number of points you wish tocalculate.For example you can sweep your circuit over a voltage range from 0 to 12 volts. Themain two sweeps that will be most important to us at this stage are the voltage sweepand the current sweep. For these two, you need to indicate to LTspice whatcomponent you wish to sweep, for example V1 or V2.

Another excellent feature of the DC sweep in LTspice, is the ability to do a nestedsweep.A nested sweep allows you to run two simultaneous sweeps to see how changes in twodifferent DC sources will affect your circuit.Once you've filled in the main sweep menu, click on the nested sweep button andchoose the second type of source to sweep and name it, also specifying the start andend values. (Note: In some versions of LTspice you need to click on enable nestedsweep). Again you can choose Linear, Octave or Decade, but also you can indicateyour own list of values, example: 1V 10V 20V. DO NOT separate the values withcommas.

NoiseE.

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LTspice will simulate noise for you either on the output or the input of the circuit.These noise calculations are performed at each frequency step and can be plotted inprobe.The two types of noise are:

Output for noise on the outputs andInput for noise on the input source.Type of Sweep (same as for AC analysis)Number of points... (same as for AC analysis)Start Frequency (same as for AC analysis)Stop Frequency (same as for AC analysis)

To use input noise you need to tell LTspice where you consider the 'input' in yourcircuit to be, for example, if your voltage source is labelled 'V1'.

DC TransferF.

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Parametric

Parametric analysis allows you to run another type of analysis (DC operating point,transient, sweeps) while using a range of component values. The best way todemonstrate this is with an example, we will use a resistor, but any other standardpart would work just as well (capacitor, inductor).

First, right click the value resistor that is to be varied. This will open a dialog boxallowing you to set "Resistor Properties". Enter the name {R} (including the curlybraces) in place of the component value.

This indicates to LTspice that the value of the resistor is a global parameter called R.Now add a spice directive to the page, by pressing the 's' key, using the icon

or the menu command

Place the box anywhere on the schematic page.Edit the directive.

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Directives always start with a period..STEP PARAM R 1k 10k 0.1k means to step the parameter R from 1kΩ to 10kΩ insteps of 0.1kΩ for every step of the outer simulation.You'll need to have one simulation command, even if it's a DC operating pointanalysis.Choose an analysis as usual, and run the simulation.If your did a non-graphical analysis, such as a DC operating point, then you'll get agraphical output which has the stepped parameter as the horizontal axis.If you did an analysis that is already graphical, such as transient, you'll get a graphwith a series of lines, one for each value of the stepped parameter. In order to isolateone trace,

use the command to "Select Steps" from the trace menu. This brings up a dialogue

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which allows you to choose which one(s) you want to show.Temperature

To do a temperature sweep, do a parametric analysis but instead of varying acomponent value, vary the temperature as follows:.STEP TEMP 0 100 1 means to step the temperature from 0°C to 100°C in steps of1°C for every step of the outer simulation.

H.

Other types of analysis There are other SPICE analyses possible. Eventually I might getthem in here, including

fourier

I.

Types of SourcesVoltage Sources A voltage source can be configured in many possible ways. Right clickingon one will bring up the "Independent Voltage Source" window. The options which show upin the window will change as the function selected changes.

(none)1.

A.V.

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This is your basic direct current voltage source that simulates a simple batteryand allows you to specify the DC voltage value.

PULSE2.

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PULSE is often used for a transient simulation of a circuit where we want to makeit act like a square wave source. It should never be used in a frequency responsestudy because LTspice assumes it is in the time domain, and therefore yourprobe plot will give you inaccurate results.

Vinitial is the value when the pulse is not "on." So for a square wave, thevalue when the wave is 'low'. This can be zero or negative as required. Fora pulsed current source, the units would be "amps" instead of "volts."Von is the value when the pulse is fully turned 'on'. This can also be zero ornegative. (Obviously, V1 and V2 should not be equal.) Again, the unitswould be "amps" if this were a current pulse.Tdelay is the time delay. The default units are seconds. The time delay maybe zero, but not negative.Trise is the rise time of the pulse. LTspice allows this value to be zero, butzero rise time may cause convergence problems in some transient analysissimulations. The default units are seconds.Tfall is the fall time in seconds of the pulse.Ton is the pulse width. This is the time in seconds that the pulse is fully on.Tperiod is the period and is the total time in seconds of the pulse.Ncycles is the number of cycles of the pulse that should happen. Leave it aszero if you want ongoing pulses.

This is a very important source for us because we do a lot of work with thesquare wave on the wave generator to see how various components and circuitsrespond to it.

SINE

A few things to note about the alternating current source. First, there are twopossible analyses which can be done and so there are two sets of parameters.For an ac analysis, the parameters are:

AC Amplitude which is the peak value of the voltage.AC Phase which is the phase angle of the voltage

3.

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For a transient analysis, the parameters are:DC offset is the DC offset voltage. It should be set to zero if you need apure sinusoid.Amplitude is the undamped amplitude of the sinusoid; i.e., the peak valuemeasured from zero no DC offset value.Freq is the frequency in Hz of the sinusoid.Tdelay is the time delay in seconds. Set this to zero for the normal sinusoid.Theta is the damping factor. (Not the phase angle!) Also set this to zerofor the normal sinusoid.This is used to apply an exponential decay to the sinusoid; theta is thedecay constant in 1/seconds.PHI is the phase advance in degrees. Set this to 90 if you need a cosinewave form.Ncycles is the number of cycles of the pulse that should happen. Leave it aszero if you want ongoing pulses.

For this analysis, LTspice takes it to be a sine source, so if you want to simulate acosine wave you need to add (or subtract) a 90° phase shift. Note that the phaseangle if left unspecified will be set by default to 0°

EXP

The EXP type of source is actually aNote that the normal usage of this source type is ...

4.

SFFM5.

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The SFFM (Single Frequency FM) type of source is actually aNote that the normal usage of this source type is ....

PWL (Piece-Wise Linear)6.

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The PWL source is a Piece Wise Linear function that you can use to create a waveform consisting of straight line segments drawn by linear interpolation betweenpoints that you define. Since you can use as many points as you want, you cancreate a very complex wave form This source type can be a voltage source or acurrent source.The syntax for this source type is flexible and has several optional parameters.The required parameters are two-dimensional points consisting of a time valueand a voltage (or current) value. There can be many of these data pairs, but thetime values must be in ascending order, and the intervals between time valuesneed not be regular.

PWL File

The PWL source is a Piece Wise Linear function that ....

7.

Current SourcesFor each of the previous discussed voltage sources, there exists the exact same sourceexcept that it produces current. There is one thing that should be mentioned; currentsources in LTspice get a little confusing. For those current sources whose circuitsymbol has an arrow, you have to point the arrow in the direction of conventionallyflowing current. This applies to all current sources, including AC and DC. Thereforeplacing the current source in the circuit backwards with seemingly incorrect polaritieswill give the correct results.An interesting little feature under the markers menu is the ability to add markers toyour circuit so you can see where the current and voltage have imaginary values in thecircuit, and the phase of your source at any point in the circuit.

B.

References and LinksIntroduction to SwitcherCAD (another name for LTspice) [PDF; Petr Kropik]This has a good step-by-step guide, including information about files and SPICE directives.

A.

LTSpice introductory manual (adding components) [PDF; Aalborg University, October 2005]This has useful information about how to add libraries and models.

B.

VI.

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SPICE overview (lots of detail) [University of Pennsylvania]Since this is about SPICE itself, rather than any particular version, such as PSpice orLTspice, the information is very widely applicable.

C.

SWCADIII (Another LTspice tutorial) (very detailed) [PDF; Aalborg University]This starts off with a lot about Switch Mode Power Supplies, i.e. what Linear Technologydesigned it for, but gets into lots of other stuff as well. (It's 257 pages long, so there reallyis a lot of stuff there.

D.

Intro to LTspice (lots of screen shots) [PDF; South Dakota School of Mines and Technology]Shorter than some of the others, but lots of screen shots

E.

Other kinds of analysis (blog) [ Chris Cross]This includes an example of varying temperature for an analysis.

F.

Other kinds of analysis (blog) [ Chris Cross]This includes an example of using WAV files for input and output of simulations.

G.

Diagonal symbols (for common components; resistor, capacitor, inductor, didode)I think that sometimes it would be nice to be able to draw things like bridge circuits in theway they're normally shown, rather than with all components either horizontal or vertical,so I created diagonal versions of the basic components.(Holding down CTRL while drawing lines allows you to make diagonal connections in theeditor.)

H.

McGraw-Hill tutorial that includes a PowerPoint presentation and lots of circuit files.I.For the more obscure questions you might have go right to the source at LinearTechnology©http://www.linear.com/designtools/software/switchercad.jsp

J.

There's a Yahoo! group which is quite active with discussions, examples etc.http://tech.groups.yahoo.com/group/LTspice/

K.

**Most of the pictures and screen shots came from Linear Technology© LTspice version 4.08o

Not related to LTspice specifically, but there is a tutorial on using LaTeX to typeset technical documents athttp://denethor.wlu.ca/latex

If you need to download Adobe Acrobat Reader go here If you need to update a browser, you might try Firefoxwhich is

freeopen sourceavailable for several platforms

Since this page uses cascading style sheets for its layout, it will look best with a browser which supports thespecifications as fully as possible.

Information on this site which is produced by Terry Sturtevant is licensed under aCreative Commons Attribution-Noncommercial-Share Alike 2.5 Canada License.

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