SpicyTL 2.0 is the latest evolution of the renowned simulation model, based on the theory of electrical circuits, that allows for predicting the electro-acoustic behavior of transmission line loudspeaker systems. Compared to the previous versions, it is able to simulate even the most complex TL configurations in a quick and intuitive way. There is no limit to the number of speakers (even different from each other) and openings that can be included in the system. The speakers can also be front-loaded with TL segments. In SpicyTL 2.0, it is possible to simulate multiple systems on the same sheet and make them interact with each other as needed. The model, particularly suitable for designing foam-damped TLs, allows for simulating frequency response, phase response, group delay, electrical impedance, cone excursion of the speakers, and air velocity at the opening. The software includes models of dual-coil speakers and passive radiators. The circuit simulation program used is LTspice by Linear Technology.
SpicyTL 2.0 is available for download in the SHOP.
Download the freeware software LTspice at the following address:
Download SpicyTL 2.0.
Open the model “01-SpicyTL-Default.asc”.
Global parameters are located in the main circuit and among these, we also find the parameters of the speakers and the passive radiator. Another global parameter is the internal width of the TL, “Line_width,” which is used to automatically calculate the length of any angular folds. Finally, there are parameters that describe some physical properties of the air and the damping materials used. Unless otherwise specified, the quantities are expressed in the units of measurement of the International System of Units (SI).
They are inserted by right-clicking on the block (sub-circuit) that you want to configure and are valid only for that block. The values should be entered in the PARAMS: row and replace the default values. A block that is copied after the parameters have been entered will retain the previously entered parameters.
List of local parameters:
S_0: area of the initial section of a segment (cm²);
S_1: area of the final section of a segment (cm²);
SL: area of the section of a straight segment; area of the initial (and final) section of a 90° bend; area of the central section of a 180° bend (cm²);
S_in: area of the initial section of a 180° bend (cm²);
S_out: area of the final section of a 180° bend (cm²);
S_foam: area of the section occupied by the foam (cm²);
S_load: area of the cone, area of the opening (cm²);
Length: length of a segment (m);
Panel_THK: thickness of the inner panel at a fold (mm);
Vol: volume (L);
output: amplitude of the sinusoidal sweep (default: 2.83 Vrms);
RG: amplifier output resistance (default: 0.1 ohm);
dist: SPL measurement distance (m);
ang: radiation angle (π steradians).
Adding a Block
Click on the Component button on the toolbar and select the SpicyTL working directory from the Top Directory dropdown menu. Select the desired block and position it in the main sheet by left-clicking with the mouse. The block can be moved, dragged, copied, or deleted like any other component using the Ltspice tools.
The blocks can be arranged horizontally or, if provided, vertically; once arranged, they connect automatically. If a particularly complex configuration requires it, the blocks can be connected with the Wire command. With the exception of the speaker, which must always be connected to an amplifier (or possibly short-circuited), disconnected and unused blocks can be left on the main sheet.
Below is an overview of the tools and blocks in SpicyTL 2.0:
It is an exclusively electrical block and does not contain acoustic components. It is not properly an amplifier, but rather a function generator suitable for testing the system. The block now contains a convenient tool that allows the user to quickly visualize the impedance curve of the speaker without the need to write expressions in the LTspice graphical post-processor; the procedure is explained below in the appropriate section.
The local parameters are:
The Speaker blocks represent the equivalent circuit of the electrical, mechanical, and acoustical components of the speaker. The speakers are named “Speaker A” and “Speaker B” and each has its own set of parameters. There is no limit to the number of speakers that can be added to the system, except for the number of available SPL labels (10 for each system). However, it is very easy to edit additional labels if needed. The presence of a node on the upper side of the block suggests that the speaker can also be front-loaded.
There is also a “Speaker A_WG” block available (the one on the far right in the image); compared to the Speaker block, it is more graphically intuitive to use if the speaker needs to be mounted inside a waveguide. This speaker obviously uses the parameters of “Speaker A”. By applying a label to the CV node, it is possible to visualize the mechanical velocity of the cone. The parameters are defined globally on the main sheet.
Dual Voice Coil Speaker
As the name suggests, it represents the equivalent circuit of the electrical, mechanical, and acoustical components of a dual voice coil speaker. This speaker can also be front-loaded and used an unlimited number of times within the system. The parameters are those of driver A.
It represents the equivalent circuit of the mechanical and acoustical components of a passive radiator. Multiple passive radiators can be installed within the same system, and the parameters are defined globally in the main sheet.
Represents a TL segment with constant, increasing, or decreasing cross-section .
The default local parameters are:
S_0=100 S_1=100 Lenght=1 S_foam=0
The “Acoustic load” block represents the acoustic model of the air load on the cone or aperture; within the block, end correction is automatically applied. On a practical level, it serves to display (again by means of the appropriate labels) the air velocity (at the opening, or on the cone surface; the latter also corresponds to the mechanical speed of the cone) and the SPL (of the loudspeaker or opening). The block must be applied to all apertures and loudspeakers that face outside the TL.
The only local parameter is the surface area (of the cone or aperture) in cm²:
It represents a 90° bend in the TL. The section variation in the fold is calculated from the input section area ‘SL’ and the global parameter ‘line_width’; the latter also serves to automatically calculate the segment length. The thickness of the inner panel in mm can be added to the total length.
In the ’90bend’ block, the area of the input section is equal to the area of the output section.
The local parameters are:
SL=100 S_foam=0 Panel_THK=0
It represents a 180° bend in the TL. The section variation in the fold is calculated from the area of the entry section ‘S_in’, the area of the middle section ‘SL’, the area of the exit section ‘S_out’ and the global parameter ‘line_width’; the latter, as in the ’90bend’ block, also serves to automatically calculate the length of the segment. The thickness of the inner panel may be added to the total length.
The local parameters are:
S_in=100 SL=100 S_out=100 S_foam=0 panel_THK=0
When placed next to a loudspeaker, it allows the effect of a coupling chamber to be quickly evaluated. If no acoustic blocks other than the driver are added, it can effectively simulate the load of a closed box.
The only local parameter is the volume, expressed in litres:
The ‘closed’ block closes the TL with a panel. It is also useful for simulating closed or bass-reflex enclosures with special geometries, taking into account internal reflections on the longest side.
There are no local parameters to enter.
There are several types of junctions available, which are very convenient for creating particularly complex configurations. These blocks are dimensionless and do not require the insertion of local parameters. The junctions can be replaced by electrical connections (Wire tool). Below is an example of their use in a folded tapped horn, with the speaker also facing forward on the TL.
Integrated TL, Integrated WG
Finally, there are two types of ‘integrated’ blocks (TL and WG). These blocks could be constructed with one loudspeaker and two TL sections, but have the advantage of automatically calculating the TL section (in the case of tapered or expanding tubes) at the point where the loudspeaker is mounted.
The labels are basically used to pick up the signals processed within the blocks. Once positioned at the indicated points, it is possible (using the Probe tool) to graphically visualise the simulations of frequency response (loudspeakers, openings and complete systems), phase response, group delay, electrical impedance, loudspeaker cone excursion and air velocity at the TL output.
There are three types of labels: SPL (relating obviously to sound pressure simulation), X (relating to cone excursion) and finally AV (relating to air velocity at the aperture).
The labels can be edited on the fly or copied from the label sets:
Run a Simulation
Click on the Run command to open the graphic display window (Probe). I recommend activating the Cartesian grid display: right-click on the graph and select View; in the submenu tick Grid. The option is saved.
The frequency response of the system is displayed automatically.
After each parameter change, the Run command should be run.
Position the probe on one of the ‘SPL’ labels. If necessary, change the vertical axis display: place the mouse on the left vertical axis of the graph and right-click. Select Bode representation in the drop-down menu and tick Decibel.
Cone Excursion Simulation
Place the probe on the ‘X’ label. The value in millivolts corresponds to the rms value of the loudspeaker excursion in millimetres. If necessary, change the vertical axis display: position the mouse over the left vertical axis of the graph and right-click. Select Bode representation in the drop-down menu and tick Linear.
Air Velocity Simulation
Place the probe on the ‘AV’ label. The value in volts corresponds to the air velocity in m/s.
The vertical axis display must be set to Bode and Linear.
After running a simulation with the Run command, we need to find the name assigned by LTspice to the points (nodes) where we are going to detect the amplifier’s output voltage and current. To do this, we must drag the amplifier slightly downwards; the connection wires to the loudspeaker are uncovered and automatically resized. We deactivate the handle by right-clicking and place the cursor (voltmeter probe) on the positive wire. We click and note down the name of the trace that appears, for example V(n001). We then move the cursor to the amplifier’s ‘+’ output: the probe becomes an ammeter and by clicking, another trace appears. We note down the name, for example Ix(x4:+). We can now delete the voltage and current traces we have just generated and type in the correct expression for the impedance display: we right-click on the box and select “Add Traces”. In the line “Expression(s) to add:” we type (in this case): V(n001)/-Ix(x4:+).
The impedance curve graph can now be obtained using the instrument built into the ‘amplifier’ block; to use the instrument, the block must be rotated 180° and connected to the loudspeaker via the ‘impedance TEST’ connection. After running the simulation, the probe placed on the positive wire (not the node) of the loudspeaker returns the impedance curve. Since this is a voltage measurement, the value is returned in volts rather than ohms.
The vertical axis display must be set to Bode and Linear.
Damping Material Parameters
In SpicyTL, it is possible to adjust various parameters that describe the physical properties of air and damping materials. From version 1.4, it is also possible to define the behaviour of the damping material at varying frequencies very accurately, thanks to the combined effect of the parameters DENS and K1.
The first parameter represents the density of the absorbing material in Kg/m³ while the second (K_1 for foam and K_2 for fibre) defines the slope of the roll-off at high frequencies.
The following graphs show the effect of the individual parameters and their combined effect (DENS 25, 30, 35 kg/m³ and K_1 200, 300, 400).