Electronic circuit simulation
Electronic circuit simulation uses mathematical models to replicate the behavior of an actual electronic device or circuit. Simulation software allows for modeling of circuit operation and is an invaluable analysis tool. Due to its highly accurate modeling capability, many
Simulating a circuit’s behavior before actually building it can greatly improve design efficiency by making faulty designs known as such, and providing insight into the behavior of electronics circuit designs. In particular, for
Some electronics simulators integrate a
Types
While there are strictly
The event driven algorithm provided by mixed-mode simulators is general-purpose and supports non-digital types of data. For example, elements can use real or integer values to simulate DSP functions or sampled data filters. Because the event driven algorithm is faster than the standard SPICE matrix solution, simulation time is greatly reduced for circuits that use event driven models in place of analog models.[5]
Mixed-mode simulation is handled on three levels; (a) with primitive digital elements that use timing models and the built-in 12 or 16 state digital logic simulator, (b) with subcircuit models that use the actual transistor topology of the
Exact representations are used mainly in the analysis of transmission line and signal integrity problems where a close inspection of an IC’s I/O characteristics is needed. Boolean logic expressions are delay-less functions that are used to provide efficient logic signal processing in an analog environment. These two modeling techniques use SPICE to solve a problem while the third method, digital primitives, use mixed mode capability. Each of these methods has its merits and target applications. In fact, many simulations (particularly those which use A/D technology) call for the combination of all three approaches. No one approach alone is sufficient.
Another type of simulation used mainly for power electronics represent piecewise linear[6] algorithms. These algorithms use an analog (linear) simulation until a power electronic switch changes its state. At this time a new analog model is calculated to be used for the next simulation period. This methodology both enhances simulation speed and stability significantly.[7]
Complexities
Process variations occur when the design is fabricated and circuit simulators often do not take these variations into account. These variations can be small, but taken together can change the output of a chip significantly.
Temperature variation can also be modeled to simulate the circuit's performance through temperature ranges.[8]
Simulation from admittance matrix
A common method of simulating linear circuits systems is with
Simple Chebyshev filter example
A fifth order, 50 ohm, Chebyshev filter with 1dB of pass band ripple and cutoff frequency of 1GHz designed using the Chebyshev Cauar topology and subsequent impedance and frequency scaling produces the elements shown in the table and Micro-cap schematic below.
element | g-value | Type | scaled for
50 ohms and 1GHz |
nodes |
---|---|---|---|---|
P1 | 1 | port | 50 | 1 |
L1 | 2.1348815 | inductor | 1.6988847E-08 | 1, 2 |
C1 | 1.0911073 | capacitor | 3.4731024E-12 | 2, 0 |
L2 | 3.0009229 | inductor | 2.3880586E-08 | 2, 3 |
C2 | 1.0911073 | capacitor | 3.4731024E-12 | 3, 0 |
L3 | 2.1348815 | inductor | 1.6988847E-08 | 3, 4 |
P2 | 1 | port | 50 | 4 |
Modeling the 2 port Y parameters
The table above provides a list of ideal elements to model along with a node attachments to simulate. Next, each non-port element must be converted into a 2X2 Y parameter model for each frequency to be simulated. For this example, a frequency of 1GHz is selected.
Elements connected to node 0, the ground node, do not need their respective Y12 or Y21 calculated, and are shown as "n/a" in the table.
element | admittance at 1GHz | Y11, Y22 at 1GHz | Y12, Y21 at 1GHz | nodes |
---|---|---|---|---|
P1 | n/a | n/a | n/a | 1 |
L1 | -J0.0093682013 | -J0.0093682013 | J0.0093682013 | 1, 2 |
C1 | j0.021822146 | j0.021822146 | n/a | 2, 0 |
L2 | -J0.0066646164 | -J0.0066646164 | J0.0066646164 | 2, 3 |
C2 | j0.021822146 | j0.021822146 | n/a | 3, 0 |
L3 | -J0.0093682013 | -J0.0093682013 | J0.0093682013 | 3, 4 |
P2 | n/a | n/a | n/a | 4 |
Inserting the 2 port Y parameters into the nodal admittance matrix
It should be remembered that while Ideal inductor and capacitor modals consist of very simple 2x2 models where Y11 = Y22 = -Y12 = -Y21, most real world elements cannot be modeled so simply. With transmission lines and real world inductor and capacitor models, for example, Y11 != -Y12, and for some more complex passive asymmetric elements Y11 != Y22. For many active linear devices, such as operational amplifiers, Y12 != Y21. Therefore, the example in this section uses independent Y11, Y12, Y21, and Y22 to illustrate the simulation processes that applies to more complex real world devices.
Each element Y parameter is inserted into the nodal admittance matrix by summing in them into the nodes they are attached to following the rules below.[9]
- Y11 is summed into the n x n node in the diagonal, where n is the node that the first pin, pin 1, is attached to.
If the second node is not 0, that is, not a ground:
- Y22 is summed into the m x m node in the diagonal, where m is the node that the second pin, pin 2, is attached to.
- Y12 is summed into the n x m node location
- Y21 is summed into the m x n node location
The table below shows the Chebyshev element 2x2 Y parameters summed in at the appropriate locations.
node | 1 | 2 | 3 | 4 |
---|---|---|---|---|
1 | L1_Y11 | L1_Y12 | ||
2 | L1_Y21 | L1_Y22+C1_Y11+L2_Y11 | L2_Y12 | |
3 | L2_Y21 | L2_Y22+C2_Y11+L3_Y11 | L3_Y12 | |
5 | L3_Y21 | L3_Y22 |
Nodal admittance matrix numerical entries
To simulate the filter at 1GHz, or any frequency, the element Y parameters must be converted to numerical entries using Y parameter models appropriate for the element installed. For ideal inductors and capacitors, the well known Y11 = Y22 = -Y12 = -Y21 = for inductors and Y11 = Y22 = -Y12 = -Y21 = for capacitors are sufficient. The numerical conversion are shown in the table below.
node | 1 | 2 | 3 | 4 |
---|---|---|---|---|
1 | -j0.0093682 | 0.0093682 | ||
2 | 0.0093682 | j0.00578933 | j0.00666462 | |
3 | j0.00666462 | j0.00578933 | 0.0093682 | |
4 | 0.0093682 | -j0.0093682 |
Removing internal nodes
Since ports are only attached to node 1 and node 4, nodes 2 and 3 need to be removed through Kron reduction. The table below shows the reduced Y parameter matrix of the Chebyshev filter example simulation after nodes 2 and 4 are eliminated. The nodes of the reduced table are renumbered to 1 and 2.
node | 1 | 2 |
---|---|---|
1 | j0.0372422 | -j0.0536574 |
2 | -j0.0536574 | j0.0372422 |
Converting to an S parameter matrix
Since the Chebyshev frequency response is observed from the S parameter matrix, namely |S12|, the next step is to convert the Y parameter matrix to an S parameter matrix, using well known Y matrix to S matrix conversions with the port impedance as the characteristic impedance (or characteristic admittance) for each node.
Simulated S parameters also allow for useful post simulation processing for things such as group delay and phase delay.
node | 1 | 2 |
---|---|---|
1 | -0.356328 + j0.280539 | 0.551322 + j0.700266 |
2 | 0.551322 + j0.700266 | -0.356328 + j0.280539 |
S parameter magnitudes
Since the Chebyshev frequency response is expected to be observable in |S12| as a 1dB equi-ripple response from 0 to 1GHz, the complex S parameter entries need to be converted to their respective magnitudes, using the standard .
node | 1 | 2 |
---|---|---|
1 | 0.45351050 | 0.89125104 |
2 | 0.89125104 | 0.45351050 |
Check the results
It may be useful to do some quick validity checks at this point. Since the example Chebyshev filter design requirement is for -1dB attenuation at the cutoff frequency of 1GHz, |S12| at 1 GHz is expected to be -1dB. Furthermore, since all simulation elements are lossless, the well known relation, |S11|2+|S12|2 = 1[10] applies at all frequencies, including 1GHz.
required condition | actual results | Status | |
---|---|---|---|
1 | 20log10(|S12|) = -1dB | 20log10(0.89125104) = -1dB | Valid |
2 | |S12|2+|S12|2 = 1 | 0.453510502+0.891251042 = 1 | Valid |
Full frequency Simulation
The final validity test for the example is to simulate the Chebyshev filter frequency response through the full useful range, which will be taken to be 100 MHz to 5 GHz for this case. This range should permit viewing of the equi-ripple |S12| of the pass band between 0 and -1 dB, somewhat steep stop band |S12| falling off at 1GHz, and an equi-ripple |S12| at the expected peak values of 20log10(.4535...) = -6.86825 dB.
Since all simulation outputs conform to the expected results, the Chebyshev filter example simulation is confirmed to be correct.
Simulating unterminated nodes
Since S parameters require terminations on all nodes being simulated, simulating the S parameter value for unterminated nodes, such as the internal nodes of a network, are technically unsupported. However, placing a resistive termination on unterminated nodes that is large enough to not introduce any error of significance to make the nodes terminated is sufficient to accurately simulate the node. For example, the two internal nodes that were eliminated above could alternatively have had a 1e+09 ohm port attached to them, so instead of using Kron reduction to eliminate the nodes, the nodes could be accurately simulated with excessively large resistive ports.
Simulating zero resistance sources
If the input source to the network is an ideal voltage source with no resistance, the example above may be made to work by including a port resistance small small enough to no introduce any error of significance. For example, a port with a resistance of 1e-09 in a network that is terminated elsewhere by 50 ohms would model an ideal source with sufficient accuracy.
Simulating the transfer function
Since the example above simulates S parameters, another conversion is necessary to obtain the transfer function from S parameters. The conversion is, .[10]
See also
Concepts:
- Lumped element model
- System isomorphism
- Transistor models
HDL:
Lists:
- List of electrical engineering software
- List of free electronics circuit simulators
- Comparison of EDA software
Software:
References
- ^ "Disadvantages and Advantages of Simulations in Online Education". Archived from the original on 2010-12-16. Retrieved 2011-03-11.
- ^ Mengue and Vignat, Entry in the University of Marne, at Vallee
- ^ Fishwick, P. "Entry in the University of Florida". Archived from the original on 2000-05-19.
- ^ Pedro, J; Carvalho, N. "Entry in the Universidade de Aveiro, Portugal" (PDF). Archived from the original (PDF) on 2012-02-07. Retrieved 2007-04-27.
- ^ L. Walken and M. Bruckner, Event-Driven Multimodal Technology Archived 2007-05-05 at the Wayback Machine
- – via IEEE Xplore.
- S2CID 111196369– via IEEE Xplore.
- ISBN 9784274902178. Retrieved October 12, 2022.
- ISBN 9781483199061.)
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: CS1 maint: date and year (link - ^ ISBN 0-89006-099-1.)
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External links
- WCCA Simple Comparing of different Methods
- Electronic circuit simulation at the Open Directory Project