Electronic Circuit Simulation: A Detailed Educational Resource

Electronic Circuit Simulation, SPICE, Verilog, VHDL, Integrated Circuit Design, Printed Circuit Board, Simulation Algorithms, Y-Matrix, S-Parameters, Transfer Function

Electronic circuit simulation is the process of using mathematical models to mimic the behavior of real-world electronic circuits or devices. This article provides a comprehensive overview of electronic circuit simulation, its importance in education and professional design, and the various types of simulators and algorithms used. It also includes a detailed example of simulating a Chebyshev filter using Y-matrix simulation techniques.

Read the original article here.

Introduction

Electronic circuit simulation is the process of using mathematical models to mimic the behavior of real-world electronic circuits or devices. This is achieved through specialized software, known as electronic circuit simulators, which allows engineers, designers, and students to model circuit operation and analyze their designs virtually. The accuracy of these simulations makes them invaluable tools in various fields, particularly in education and professional circuit design.

Electronic Circuit Simulation: The use of computer software to model and analyze the behavior of electronic circuits before they are physically built. This involves using mathematical algorithms and models to represent electronic components and their interactions within a circuit.

In educational settings, electronic circuit simulation software is widely adopted in colleges and universities for electronics technician and engineering programs. Its interactive nature actively engages learners, promoting deeper understanding through analysis, synthesis, organization, and evaluation of electronic concepts. This hands-on approach facilitates the construction of knowledge as students experiment and observe circuit behavior in a virtual environment.

Beyond education, circuit simulation plays a critical role in improving design efficiency. By simulating a circuit’s behavior before physical construction, designers can:

• Identify and rectify faulty designs: Simulation reveals potential flaws and weaknesses in a design early in the process, preventing costly errors and rework later on.
• Gain insights into circuit behavior: Simulations provide a detailed understanding of how a circuit will operate under various conditions, allowing for optimization and performance enhancement.

This is particularly crucial for integrated circuits (ICs), where the stakes are high:

Integrated Circuit (IC): Also known as a microchip or chip, an IC is a set of electronic circuits on one small flat piece (or “chip”) of semiconductor material, typically silicon.

• Expensive Tooling (Photomasks): The creation of photomasks, which are essential for manufacturing ICs, is a highly expensive process. Simulation minimizes the risk of errors that could necessitate costly revisions to these masks.

Photomask: A transparent plate used in photolithography to selectively block light that illuminates the semiconductor wafer during the IC fabrication process. It essentially acts as a stencil for transferring circuit patterns onto the silicon chip.

• Impractical Breadboards: Building prototype circuits on breadboards is often impractical for complex IC designs due to their miniature scale and intricate interconnections.

Breadboard: A solderless prototyping board used to build temporary circuits for experimentation and testing. Components are inserted into sockets, and connections are made using jumper wires.

• Difficult Internal Signal Probing: Accessing and measuring signals within an IC is extremely challenging due to the microscopic size and internal structure of the chip. Simulation overcomes this limitation by providing complete visibility into all circuit nodes and signals.

Therefore, simulation is not just a helpful tool but a fundamental necessity in modern IC design. Two of the most recognized types of simulators are:

• SPICE (Simulation Program with Integrated Circuit Emphasis): A widely used analog electronic circuit simulator.

SPICE (Simulation Program with Integrated Circuit Emphasis): A general-purpose analog electronic circuit simulator that is used to verify the integrity of circuit designs and to predict circuit behavior. It is considered the industry standard for analog circuit simulation.

• Verilog and VHDL (VHSIC Hardware Description Language) based simulators: Primarily used for digital circuit simulation.

Verilog and VHDL (VHSIC Hardware Description Language): Hardware description languages (HDLs) used to model, design, simulate, and verify electronic systems, most commonly digital circuits at the register-transfer level of abstraction.

Integrated Simulation Environments

Many modern electronic circuit simulators offer a comprehensive integrated environment that streamlines the design and simulation workflow. These environments typically combine:

• Schematic Editor: A graphical interface for drawing and editing circuit diagrams. This allows users to visually represent their circuit designs by placing and connecting components.
• Simulation Engine: The core of the simulator, responsible for performing the mathematical calculations based on the circuit description and component models. This engine solves the circuit equations to predict the circuit’s electrical behavior over time or frequency.
• On-screen Waveform Display: A graphical tool for visualizing simulation results, typically showing voltage and current waveforms as a function of time. This allows designers to immediately observe the effects of circuit modifications on the output.

This integrated approach enables designers to rapidly iterate on their designs. They can modify the schematic in the editor, initiate a new simulation, and instantly observe the impact of their changes on the waveform display.

Component and Device Libraries

To accurately simulate circuits, simulators rely on extensive libraries of models representing various electronic components and devices. These libraries typically include:

• IC-Specific Transistor Models: Sophisticated models like BSIM (Berkeley Short-channel IGFET Model) that accurately represent the behavior of transistors within integrated circuits, taking into account complex effects like short-channel effects and velocity saturation.

BSIM (Berkeley Short-channel IGFET Model): A widely used industry-standard model for MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) devices, particularly for advanced CMOS (Complementary Metal-Oxide-Semiconductor) technologies used in integrated circuits.

• Generic Components: Models for basic electronic components such as resistors, capacitors, inductors, and transformers, with varying levels of complexity and accuracy.
• User-Defined Models: The flexibility to incorporate custom models, allowing users to represent specialized components or behaviors not included in standard libraries. These can include:
  • Controlled Current and Voltage Sources: Ideal or non-ideal sources whose output is dependent on another voltage or current in the circuit.
  • Models in Verilog-A or VHDL-AMS: Using hardware description languages to define custom analog and mixed-signal component models for advanced simulations.

PCB-Specific Models

Designing Printed Circuit Boards (PCBs) requires specialized models that account for the unique characteristics of PCB traces and interconnections.

Printed Circuit Board (PCB): A board that mechanically supports and electrically connects electronic components using conductive tracks, pads and other features etched from copper sheets laminated onto a non-conductive substrate.

• Transmission Line Models: Models that represent PCB traces as transmission lines, considering effects like signal reflection, impedance mismatch, and propagation delay, especially important for high-speed signals.
• IBIS Models (Input/Output Buffer Information Specification): Behavioral models for the input and output buffers of digital integrated circuits, used to simulate signal integrity and analyze signal reflections and crosstalk on PCBs.

IBIS Models (Input/Output Buffer Information Specification): A standard for describing the analog behavior of digital IC input/output buffers. IBIS models are used for signal integrity analysis to predict signal quality and timing in high-speed digital circuits.

Types of Electronic Circuit Simulators

Electronic circuit simulators can be broadly categorized based on their simulation capabilities and algorithms.

1. Analog Simulators:

These simulators, like SPICE, are designed primarily for simulating circuits composed of analog components such as transistors, resistors, capacitors, and inductors. They use numerical methods to solve circuit equations in the time or frequency domain, providing detailed analysis of voltage and current waveforms.

2. Digital Simulators:

Digital simulators, often based on Verilog or VHDL, focus on simulating digital circuits composed of logic gates, flip-flops, and other digital building blocks. They typically use event-driven algorithms to efficiently simulate the discrete changes in digital signals.

3. Mixed-Mode or Mixed-Signal Simulators:

Popular modern simulators often integrate both analog and digital simulation capabilities into a single environment. These are known as mixed-mode or mixed-signal simulators.

Mixed-Mode/Mixed-Signal Simulators: Electronic circuit simulators that can simulate circuits containing both analog and digital components simultaneously. This allows for the analysis of complex systems that combine analog and digital functionalities, such as ADCs (Analog-to-Digital Converters) and DACs (Digital-to-Analog Converters).

Key features of mixed-mode simulators include:

• Simultaneous Simulation: They can simulate both analog and digital portions of a circuit concurrently, providing a holistic view of the system’s behavior.
• Integrated Schematic: A single schematic can encompass both analog and digital components, simplifying the design process.
• Timing Models for Digital Components: Digital models accurately represent propagation delays, rise times, and fall times, crucial for timing analysis in digital circuits.

4. Event-Driven Simulation:

Mixed-mode simulators often employ event-driven algorithms for simulating digital parts of the circuit.

Event-Driven Algorithm: A simulation technique primarily used for digital circuits where the simulator only processes changes in signal values (events) rather than simulating the entire circuit at every time step. This significantly speeds up simulation for digital circuits where activity is often sparse.

This approach offers advantages:

• General-Purpose: Event-driven algorithms are not limited to digital signals and can handle non-digital data types like real or integer values. This enables the simulation of systems incorporating Digital Signal Processing (DSP) functions or sampled data filters within a mixed-signal context.
• Faster Simulation: Event-driven simulation is generally faster than the standard SPICE matrix solution for circuits with significant digital content. This is because the simulator only processes events, leading to computational efficiency, especially in circuits where digital components are less frequently switching.

Levels of Mixed-Mode Simulation:

Mixed-mode simulation can be implemented at three levels of abstraction:

• Primitive Digital Elements with Timing Models: Using built-in digital primitives (like AND, OR, NOT gates) that incorporate timing models (propagation delay, rise/fall times) and often utilize a 12 or 16-state digital logic simulator for accurate digital signal representation.
• Subcircuit Models with Transistor Topology: Employing detailed subcircuit models for digital blocks, representing them at the transistor level (using MOSFET models, for example). This provides higher accuracy for digital sections by simulating the actual transistor behavior within the digital gates.
• Inline Boolean Logic Expressions: Using delay-less Boolean logic expressions directly within the schematic to represent simple digital logic functions. This provides an efficient way to model logic signal processing in an analog environment without the overhead of detailed digital models, suitable for control logic or simple digital interfaces.

5. Piecewise Linear Algorithms for Power Electronics Simulation:

For power electronics circuits, which often involve switching devices like diodes and transistors, piecewise linear algorithms are frequently used.

Piecewise Linear Algorithm: A simulation technique that approximates the behavior of non-linear components (like power electronic switches) using linear segments. The simulation proceeds linearly until a switch changes state, at which point a new linear model is calculated for the next simulation period.

This method offers benefits for power electronics simulation:

• Enhanced Simulation Speed: Piecewise linear simulation is generally faster than traditional analog simulation for circuits with switching elements, as it avoids computationally intensive non-linear equation solving during periods when the switch state is constant.
• Improved Stability: It can improve simulation stability, especially for circuits with abrupt switching transitions, by handling the switch state changes in a controlled manner.

Complexities in Electronic Circuit Simulation

While circuit simulation is a powerful tool, it’s important to be aware of its limitations and the complexities that can arise:

1. Process Variations:

During the manufacturing process of integrated circuits, variations in parameters like transistor dimensions and doping concentrations inevitably occur. These process variations are usually not accounted for in standard circuit simulations.

Process Variations: In semiconductor manufacturing, process variations refer to the unavoidable deviations in device parameters and physical dimensions that occur during fabrication. These variations can affect circuit performance and yield.

Even small variations, when combined across numerous components in a complex IC, can significantly impact the final circuit performance and characteristics. Advanced simulation techniques, like Monte Carlo simulation, are used to analyze the impact of process variations by running multiple simulations with randomly varied component parameters within specified statistical distributions.

2. Temperature Variation:

The performance of electronic components is temperature-dependent. Simulators can model the effects of temperature variation on circuit behavior.

Temperature Variation: Changes in the operating temperature of electronic components and circuits. Temperature affects various device parameters, such as transistor mobility, threshold voltage, and resistor values, influencing circuit performance.

By simulating circuits across a range of temperatures, designers can assess circuit stability, performance drift, and reliability under different operating conditions. Temperature-dependent models for components are used to capture these effects accurately.

Simulation from Admittance Matrix (Y-Matrix)

A common technique for simulating linear circuits, especially in the frequency domain, is based on admittance matrices, also known as Y-matrices.

Admittance Matrix (Y-Matrix): A matrix representation of a linear circuit that describes the relationship between currents entering and voltages at different nodes in the circuit. The Y-matrix is particularly useful for analyzing circuits in the frequency domain.

The process involves several steps:

1. Modeling Components as N-Port Y-Matrices: Each linear component in the circuit is represented as an N-port network, and its behavior is described by an N x N Y-matrix.

N-Port Network: A circuit or component with N terminals (ports) where energy can enter or leave the system. For example, a resistor is a 2-port network, while a transistor can be considered a 3-port or 4-port network.

2. Inserting Component Y-Matrices into Nodal Admittance Matrix: The Y-matrices of individual components are incorporated into the nodal admittance matrix of the entire circuit. This matrix represents the overall circuit connectivity and component admittances.

Nodal Admittance Matrix: A square matrix that represents the admittance relationships between the nodes of an electrical circuit. It is a key element in nodal analysis, a method for solving circuit equations.

3. Installing Port Terminations: Ports are added at nodes where external connections or terminations are required (e.g., input and output ports).

Port: A pair of terminals in an electrical circuit where energy can be supplied or extracted. Ports are used to connect a circuit to external systems or measurement instruments.

4. Kron Reduction (Eliminating Internal Nodes): If there are nodes in the circuit that are not ports (internal nodes), Kron reduction is used to eliminate these nodes from the nodal admittance matrix. This simplifies the matrix and reduces the computational complexity without affecting the port behavior.

Kron Reduction: A matrix reduction technique used in circuit analysis to eliminate internal nodes from a network and obtain a reduced network representation in terms of only the external ports.

5. Converting Y-Matrix to S or Z Matrix (as needed): The resulting Y-matrix can be converted to other network parameter matrices, such as the scattering matrix (S-matrix) or impedance matrix (Z-matrix), depending on the desired analysis.

Scattering Matrix (S-Matrix): A matrix that describes the reflection and transmission characteristics of a linear network when terminated in specific impedances. S-parameters are widely used in high-frequency circuit analysis and microwave engineering.

Impedance Matrix (Z-Matrix): A matrix representation of a linear circuit that relates voltages at different nodes to currents entering those nodes. The Z-matrix is another way to characterize the network behavior, alternative to the Y-matrix.

6. Extracting Desired Measurements: Finally, desired circuit characteristics, such as impedance, gain, or reflection coefficients, are extracted from the Y, Z, or S matrices.

Simple Chebyshev Filter Example

To illustrate the Y-matrix simulation process, consider a fifth-order Chebyshev filter design example.

Chebyshev Filter: A type of electronic filter known for its steep roll-off in the stopband and equi-ripple behavior in either the passband or stopband (or both). Chebyshev filters offer a sharper transition between passband and stopband compared to Butterworth filters of the same order.

This example designs a 5th order, 50-ohm Chebyshev filter with 1dB passband ripple and a cutoff frequency of 1GHz, using the Chebyshev Cauer topology.

Passband Ripple: The maximum allowed fluctuation in the gain or attenuation within the passband of a filter. It is a specification that defines the acceptable variation in signal level within the desired frequency range.

Cutoff Frequency: The frequency at which the filter’s attenuation reaches a specified level (typically -3dB for a low-pass filter). It marks the boundary between the passband and stopband of the filter.

Modeling the 2-Port Y-Parameters

For each component in the Chebyshev filter circuit, a 2x2 Y-parameter model is created for the chosen simulation frequency (e.g., 1 GHz). The table below represents the ideal elements and their node attachments for simulation.

(Note: The original article refers to a table and schematic which are not available in the provided text. To fully illustrate this section, a table and schematic would be needed outlining the Chebyshev filter components and their connections.)

For components connected to node 0 (ground), the Y12 and Y21 parameters are often not needed and are marked as “n/a”.

Inserting 2-Port Y-Parameters into the Nodal Admittance Matrix

It’s crucial to remember that while ideal inductors and capacitors have simple 2x2 Y-parameter models (where Y11 = Y22 = -Y12 = -Y21), real-world components are more complex. For transmission lines and real components, Y11 may not equal -Y12, and for asymmetric components, Y11 may not equal Y22. Active devices like operational amplifiers can also have unequal off-diagonal Y-parameters (Y12 ≠ Y21).

The Y-parameters for each component are inserted into the nodal admittance matrix by summing them into the matrix entries corresponding to the nodes they are connected to, following these rules:

• Y11: Added to the diagonal entry (n, n) of the nodal admittance matrix, where ‘n’ is the node number connected to pin 1 of the component.
• Y22 (if node 2 is not ground): Added to the diagonal entry (m, m) of the nodal admittance matrix, where ‘m’ is the node number connected to pin 2 of the component.
• Y12: Added to the off-diagonal entry (n, m) of the nodal admittance matrix.
• Y21: Added to the off-diagonal entry (m, n) of the nodal admittance matrix.

(Again, the original article mentions a table showing the Chebyshev element 2x2 Y-parameters summed into the nodal admittance matrix, which is not available in the provided text.)

Nodal Admittance Matrix Numerical Entries

To perform a numerical simulation, the symbolic Y-parameters must be converted into numerical values at the chosen simulation frequency (e.g., 1 GHz). For ideal inductors and capacitors, simplified formulas can be used:

• Inductor: Y11 = Y22 = -Y12 = -Y21 = j2πfL
• Capacitor: Y11 = Y22 = -Y12 = -Y21 = -j/(2πfC)

where:

• j is the imaginary unit
• π is pi (approximately 3.14159)
• f is the simulation frequency
• L is the inductance
• C is the capacitance

(The article mentions a table showing numerical conversion of Y-parameters, which is not provided in the text.)

Removing Internal Nodes (Kron Reduction)

If there are internal nodes in the circuit that are not ports (like nodes 2 and 3 in the Chebyshev example), Kron reduction is applied to eliminate them from the nodal admittance matrix. This results in a reduced Y-matrix that only represents the behavior at the ports (nodes 1 and 4, renumbered to 1 and 2 after reduction).

(The article refers to a table showing the reduced Y-parameter matrix after Kron reduction, not available in the provided text.)

Converting to an S-Parameter Matrix

For frequency response analysis, particularly for filters, the S-parameter matrix is often preferred. The Y-matrix is converted to an S-matrix using well-established Y-to-S matrix conversion formulas. This conversion requires specifying the characteristic impedance (or admittance) for each port. In the Chebyshev example, a 50-ohm characteristic impedance is used.

S-Parameter Magnitudes

The S-parameter matrix elements are generally complex numbers. To analyze the frequency response, the magnitudes of the S-parameters are calculated using the formula:

|S_ij| = √(S_{ij_real}² + S_{ij_imag}²)

For filter analysis, the magnitude of S₁₂ (|S₁₂|), representing the transmission coefficient, is of primary interest.

Checking the Results

After simulation, it’s important to perform validity checks to ensure the results are reasonable and consistent with expectations. For the Chebyshev filter example:

• Attenuation at Cutoff Frequency: At 1 GHz (cutoff frequency), |S₁₂| should be approximately -1dB, matching the design specification.
• Lossless Condition: Since ideal, lossless components are used in this example, the relationship |S₁₁|² + |S₁₂|² = 1 should hold true across all frequencies, including 1 GHz. This confirms energy conservation in the simulation.

Full Frequency Simulation

To fully validate the Chebyshev filter design, a full frequency simulation is performed over a wider frequency range (e.g., 100 MHz to 5 GHz). This allows for:

• Equi-ripple Passband: Observing the 1dB equi-ripple behavior of |S₁₂| in the passband (0 to 1 GHz).
• Stopband Roll-off: Verifying the steep roll-off of |S₁₂| beyond 1 GHz in the stopband.
• Stopband Peak Values: Confirming the expected peak values of |S₁₂| in the stopband (around -6.87 dB for this design).

If the simulation results align with these expected characteristics, the Chebyshev filter simulation is considered valid and correct.

Simulating Unterminated Nodes

S-parameter simulation technically requires all nodes to be terminated. Simulating unterminated nodes (internal nodes without terminations) is not directly supported. However, a practical workaround is to add a very large resistive termination to such nodes.

By connecting a large resistor (e.g., 1e+09 ohms) to an unterminated node, it effectively becomes terminated for simulation purposes without significantly affecting the circuit’s behavior. This allows for accurate simulation of internal nodes without using Kron reduction.

Simulating Zero Resistance Sources

Similarly, ideal voltage sources with zero internal resistance can cause issues in some simulators. To simulate a near-ideal voltage source, a very small series resistance can be added to the source.

Using a small resistance (e.g., 1e-09 ohms) in series with the voltage source, especially in circuits with higher impedance terminations (e.g., 50 ohms), effectively models an ideal voltage source without causing simulation problems.

Simulating the Transfer Function

While S-parameters are useful for frequency response analysis, the transfer function (voltage gain or attenuation) is often desired.

Transfer Function: A mathematical function that describes the relationship between the output and input of a system in the frequency domain. In circuit analysis, the transfer function typically represents the voltage gain or current gain of a circuit as a function of frequency.

The transfer function (V_i/V_j) can be derived from the S-parameters using the following conversion formula:

(V_i/V_j) = (S_ij / 2) * √(R_j / R_i) (for i ≠ j)

where:

• R_i and R_j are the port resistances at ports i and j, respectively.

This conversion allows designers to obtain the voltage gain or attenuation characteristics of the circuit from the S-parameter simulation results.

See also

• Circuit design
• Electronic design automation
• Hardware description language
• List of free electronics circuit simulators
• Mixed-signal integrated circuit
• OpSim Message Passing Simulator
• PSpice
• Signal integrity
• Comparison of EDA software

References

(The original article lists references, which are not included in the provided text. In a full educational resource, these references would be listed here for further reading.)

External links

• [WCCA Simple Comparing of different Methods](Link to External Resource - if available)
• [Electronic circuit simulation at the Open Directory Project](Link to External Resource - if available)

(Note: The provided external links might need to be verified and updated for a complete educational resource.)