CapaCalc

Calculates the electrical capacitance of a variety of conductor arrangements:

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README

CapaCalc

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Introduction

CapaCalc is a desktop application designed to compute the electrical capacitance for several common conductor configurations and capacitor network arrangements. It is developed using Free Pascal and Lazarus IDE, requiring no external third-party components. The calculations cover fundamental geometries, series/parallel combinations, and the capacitance of a semiconductor p/n junction. The application provides a graphical user interface (GUI) for easy interaction and displays relevant formulas and geometries where applicable.

Supported Capacitance Calculations

CapaCalc provides detailed calculations for the following conductor arrangements and circuits. For each type, the formula used by the application, the required inputs, generated outputs, relevant source files, and validation rules are described. Code snippets illustrate how the core calculation is implemented.

Parallel Plate Capacitor

Description: Calculates the capacitance of two parallel conducting plates separated by a dielectric material. This is a fundamental model for many capacitor designs.
Source Files: source/ccplanarcapframe.pas, source/ccplanarcapframe.lfm
Inputs:
- Plate distance (d) [Code variable: d]
- Plate length (L) [Code variable: L]
- Plate width (B) [Code variable: W]
- Dielectric constant (k) [Code variable: eps]
- Input units for d, L, B (Length Units, selected by user)
- Input units for output Area (Area Units, selected by user)
- Input units for output Capacitance, Capacitance per area, Capacitance per length (Capa Units, selected by user)
Outputs:
- Area [Code variable: A] (Calculated as W * L)
- Capacitance (C) [Code variable: capa]
- Capacitance per area (Calculated as capa / A)
- Capacitance per length (Calculated as capa / L)
- Output units are selected by the user for Area and Capacitance. Capacitance per area/length units are derived and displayed.
Formula: The capacitance $C$ is calculated using the standard formula for a parallel plate capacitor: $$C = \epsilon_0 \epsilon_r \frac{A}{d}$$ where $\epsilon_0$ is the permittivity of free space, $\epsilon_r$ is the relative dielectric constant (input 'k'), $A$ is the area of the plates ($L \times B$), and $d$ is the distance between the plates.
Validation (TPlanarCapFrame.ValidData): Distance (d), Length (L), and Width (W) must be positive numbers. Dielectric constant (k / eps) must be a number. All unit comboboxes (Dist, Length, Width, Area, Capa) must have a selected value.
Real-World Idea: This model is used extensively in designing printed circuit board (PCB) traces as capacitors, parallel plate capacitors for energy storage, or estimating parasitic capacitance between conducting layers.

Spherical Capacitor

Description: Calculates the capacitance of a spherical capacitor, which consists of two concentric conducting spheres of radii $a$ and $b$ ($b > a$) separated by a dielectric medium.
Source Files: source/ccsphericalcapframe.pas, source/ccsphericalcapframe.lfm (inherits from ccBaseFrame)
Inputs:
- Inner radius (a) [Code variable: ra]
- Outer radius (b) [Code variable: rb]
- Dielectric constant (k) [Code variable: eps]
- Input units for a, b (Length Units, selected by user)
- Input units for output Area (Area Units, selected by user)
- Input units for output Capacitance, Capacitance per area (Capa Units, selected by user)
Outputs:
- Area [Code variable: A] (Calculated as 1.0/6.0 * pi *(ra + rb)*(ra + rb)*(ra + rb). Clarification: This calculated value is not a standard geometric area (like the surface area of either sphere or the gap between them). It appears to be derived from an intermediate term in a different, possibly volume-related, context. Its primary purpose in the UI is as the denominator for calculating "Capacitance per area" for display purposes. This "Capacitance per area" is therefore also based on this non-standard 'Area' value and should be interpreted with caution regarding standard physical units like F/m². The core, meaningful output for this geometry is the total Capacitance (C).)
- Capacitance (C) [Code variable: Capa]
- Capacitance per area (Calculated as Capa / A, using the non-standard 'Area' value)
- Output units are selected by the user.
Formula: The capacitance $C$ is calculated using the standard formula for a spherical capacitor:

$$C = 4 \pi \epsilon_0 \epsilon_r \frac{ab}{b-a} = 4 \pi \epsilon_0 \epsilon_r \frac{1}{\frac{1}{a} - \frac{1}{b}}$$ where $\epsilon_0$ is the permittivity of free space, $\epsilon_r$ is the relative dielectric constant (input 'k'), $a$ is the inner radius, and $b$ is the outer radius.

Validation (TSphericalCapFrame.ValidData): Inner radius (a), Outer radius (b), and Dielectric constant (k / eps) must be numbers. Both radii must be positive. The inner radius (a) must be strictly smaller than the outer radius (b). All unit comboboxes (Radius A, Radius B, Area, Capa) must have a selected value.
Real-World Idea: Used in the design of some high-voltage electrodes, ionization chambers, or as a conceptual model in electrostatics.

Cylindrical Capacitor

Description: Calculates the capacitance of a cylindrical capacitor, typically consisting of two concentric conducting cylinders of radii $a$ and $b$ ($b > a$) and length $L$, separated by a dielectric. This geometry is characteristic of coaxial cables.
Source Files: source/cccylindricalcapframe.pas, source/cccylindricalcapframe.lfm (inherits from TSphericalCapFrame for UI elements and some methods, but overrides Calculate and related properties/methods)
Inputs:
- Inner radius (a) [Code variable: ra (inherited)]
- Outer radius (b) [Code variable: rb (inherited)]
- Length (L) [Code variable: L]
- Dielectric constant (k) [Code variable: eps (inherited)]
- Input units for a, b, L (Length Units, selected by user)
- Input units for output Area (Area Units, selected by user)
- Input units for output Capacitance, Capacitance per area, Capacitance per length (Capa Units, selected by user)
Outputs:
- Area [Code variable: A] (Calculated as $\pi (ra + rb) L$. Clarification: This calculated value is not the standard geometric area used in the analytical capacitance formula ($2\pi a L$ or $2\pi b L$). It represents a simplified surface area calculation ($\pi$ times the sum of radii times length), which is used as the denominator for calculating "Capacitance per area" for display purposes. The "Capacitance per area" output is therefore based on this non-standard 'Area' value and should be interpreted with caution. The primary standard output for this geometry is the total Capacitance (C) or, more commonly for transmission lines, the Capacitance per length.)
- Capacitance (C) [Code variable: capa]
- Capacitance per area (Calculated as capa / A, using the non-standard 'Area' value)
- Capacitance per length (Calculated as capa / L)
- Output units are selected by the user.
Formula: The capacitance $C$ is calculated using the standard formula for a cylindrical capacitor:

$$C = 2 \pi \epsilon_0 \epsilon_r \frac{L}{\ln(\frac{b}{a})}$$ where $\epsilon_0$ is the permittivity of free space, $\epsilon_r$ is the relative dielectric constant (input 'k'), $L$ is the length, $a$ is the inner radius, and $b$ is the outer radius.

Validation (TCylindricalCapFrame.ValidData): Inner radius (a), Outer radius (b), Length (L), and Dielectric constant (k / eps) must be numbers. All inputs must be positive. The inner radius (a) must be strictly smaller than the outer radius (b). All unit comboboxes (Radius A, Radius B, Length, Area, Capa) must have a selected value.
Real-World Idea: Essential for designing and analyzing coaxial cables used in communication and RF systems, or cylindrical capacitors for power electronics.

Capacitance between Rectangular Conductor and Conducting Plane

Description: Calculates the capacitance between a rectangular conductor placed parallel to and above a large conducting plane (ground plane). This configuration is relevant in microstrip lines and estimating parasitic capacitance.
Source Files: source/cclineplanecapframe.pas, source/cclineplanecapframe.lfm (inherits from TPlanarCapFrame for UI structure, but overrides Calculate, ValidData, and related properties/methods)
Inputs:
- Distance (d) from the conductor's bottom to the plane [Code variable: d]
- Conductor length (L) [Code variable: L]
- Conductor width (B) [Code variable: W]
- Conductor height (H) [Code variable: H]
- Dielectric constant (k) [Code variable: eps]
- Input units for d, L, B, H (Length Units, selected by user)
- Input units for output Capacitance, Capacitance per length (Capa Units, selected by user)
Outputs:
- Capacitance (C) [Code variable: capa]
- Capacitance per length (Calculated as capa / L)
- Output units are selected by the user.
Formula: The capacitance $C$ is calculated using an approximate formula suitable for microstrip-like geometries:

$$C = \epsilon_0 \epsilon_r L \left(\frac{B}{d} + 0.77 + 1.06\sqrt{\sqrt{\frac{B}{d}}} + 1.06\sqrt{\frac{H}{d}}\right)$$ where $\epsilon_0$ is the permittivity of free space, $\epsilon_r$ is the relative dielectric constant (input 'k'), $L$ is the conductor length, $B$ is the conductor width, and $H$ is the conductor height, and $d$ is the distance to the plane.

Validation (TLinePlaneCapFrame.ValidData): Distance (d), Length (L), Width (B), and Height (H) must be positive numbers. Dielectric constant (k / eps) must be a number. All unit comboboxes (Dist, Length, Width, Height, Capa) must have a selected value.
Accuracy Note: The formula used is an approximation. The accuracy is noted in the application based on the ratios of conductor width (B) to distance (d) (Wd) and conductor height (H) to distance (d) (Hd). Refer to the SAccuracy2Percent, SAccuracy6Percent, and SInaccurate strings in ccStrings.pas and the logic in TLinePlaneCapFrame.Calculate for the specific conditions.
Real-World Idea: Calculating the capacitance of a microstrip line on a PCB, where the rectangular conductor is the trace and the plane is the ground layer.

Capacitance between Cylindrical Conductor and Conducting Plane

Description: Calculates the capacitance between a cylindrical conductor placed parallel to and above a large conducting plane (ground plane).
Source Files: source/cccylplanecapframe.pas, source/cccylplanecapframe.lfm (inherits from ccBaseFrame)
Inputs:
- Line center-to-plane distance (d) [Code variable: d]
- Cylinder radius (r) [Code variable: R]
- Length (L) [Code variable: L]
- Dielectric constant (k) [Code variable: eps]
- Input units for d, r, L (Length Units, selected by user)
- Input units for output Capacitance, Capacitance per length (Capa Units, selected by user)
Outputs:
- Capacitance (C) [Code variable: Capa] (Calculated by the DoCalc function, which includes the length L. The application then calculates 'Capacitance per length' by dividing this result by L.)
- Capacitance per length (Calculated as Capa / L)
- Output units are selected by the user.
Formula: The capacitance $C$ is calculated using the method of images, yielding the formula:

$$C = 2 \pi \epsilon_0 \epsilon_r \frac{L}{\ln\left(\frac{d + \sqrt{d^2 - r^2}}{r}\right)}$$ where $\epsilon_0$ is the permittivity of free space, $\epsilon_r$ is the relative dielectric constant (input 'k'), $L$ is the length, $d$ is the distance from the cylinder center to the plane, and $r$ is the cylinder radius.

Validation (TCylPlaneCapFrame.ValidData): Distance (d), Radius (r), Length (L), and Dielectric constant (k / eps) must be numbers. All inputs must be positive. The radius (r) must be strictly smaller than the distance (d). The term d*d - R*R inside the square root must be non-negative, which is guaranteed if d > R. The argument of the logarithm (d + sqrt(d*d - R*R))/R must be positive. All unit comboboxes (Dist, Radius, Length, Capa) must have a selected value.
Real-World Idea: Estimating parasitic capacitance between a wire and a ground plane, or modeling the capacitance of single transmission lines.

Capacitance between Two Cylinders

Description: Calculates the capacitance between two parallel cylindrical conductors. This is relevant for twin-lead transmission lines or estimating coupling between wires.
Source Files: source/cc2cylcapframe.pas (inherits from ccCylPlaneCapFrame for UI elements and some methods, but overrides DoCalc and ValidData), source/cccylplanecapframe.pas (defines the inherited Calculate method), source/cc2cylcapframe.lfm (inherits from ccCylPlaneCapFrame.lfm)
Inputs:
- Center-to-center distance (d) [Code variable: d (inherited from ccCylPlaneCapFrame)]
- Cylinder radius (R) [Code variable: R (inherited from ccCylPlaneCapFrame)]
- Length (L) [Code variable: L (inherited from ccCylPlaneCapFrame)]
- Dielectric constant (k) [Code variable: eps (inherited from ccCylPlaneCapFrame)]
- Input units for d, R, L (Length Units, selected by user)
- Input units for output Capacitance, Capacitance per length (Capa Units, selected by user)
Outputs:
- Capacitance (C) [Code variable: Capa (in ccCylPlaneCapFrame.pas)] (Calculated by the overridden DoCalc function in TTwoCylCapFrame.pas, which includes the length L. The application then calculates 'Capacitance per length' by dividing this result by L.)
- Capacitance per length (Calculated as Capa / L)
- Output units are selected by the user.
Formula: The capacitance $C$ between two parallel cylinders is calculated using the formula:

$$C = \pi \epsilon_0 \epsilon_r \frac{L}{\ln\left( \frac{d/2 + \sqrt{(d/2)^2 - R^2}}{R} \right)}$$ where $\epsilon_0$ is the permittivity of free space, $\epsilon_r$ is the relative dielectric constant (input 'k'), $L$ is the length, $d$ is the center-to-center distance, and $R$ is the cylinder radius.

Validation (TTwoCylCapFrame.ValidData): Center-to-center distance (d), Radius (R), Length (L), and Dielectric constant (k / eps) must be numbers. R and d must be positive. Half of the distance (d/2) must be strictly greater than the radius (R). The term (d/2)^2 - R^2 inside the square root must be non-negative, which is guaranteed if d/2 > R. The argument of the logarithm (d/2 + sqrt((d/2)^2 - R^2))/R must be positive. All unit comboboxes (Dist, Radius, Length, Capa) must have a selected value.
Real-World Idea: Modeling twin-lead transmission lines or estimating the coupling capacitance between adjacent wires in a bundle.

Capacitors in Series

Description: Calculates the equivalent total capacitance of multiple capacitors connected in series. The application supports up to 8 individual capacitors.
Source Files: source/ccseriescapframe.pas (inherits from ccManyCapFrame), source/ccmanycapframe.pas, source/ccseriescapframe.lfm (inherits from ccManyCapFrame.lfm)
Inputs:
- Up to 8 individual capacitance values (C1 to C8) [Code variables: FEditArray - an array of TEdit in TManyCapFrame]
- Important: All input capacitance values should be in the same units. The application displays a reminder "Same units!".
Outputs:
- Total capacitance (C) [Code variable: capa in TManyCapFrame]
- The number of decimal places for the output can be adjusted using an up/down control.
Formula: The total capacitance $C_{total}$ for $n$ capacitors connected in series is calculated using the reciprocal of the sum of the reciprocals of individual capacitances:

$$\frac{1}{C_{total}} = \sum_{i=1}^{n} \frac{1}{C_i} \quad \implies \quad C_{total} = \frac{1}{\sum_{i=1}^{n} \frac{1}{C_i}}$$

Validation (TManyCapFrame.ValidData): Any non-empty input fields must contain positive numbers.
Real-World Idea: Analyzing voltage division across capacitors in AC circuits, or calculating the effective capacitance of components fabricated on different layers in microelectronics.

Capacitors in Parallel

Description: Calculates the equivalent total capacitance of multiple capacitors connected in parallel. The application supports up to 8 individual capacitors.
Source Files: source/ccparallelcapframe.pas (inherits from ccManyCapFrame), source/ccmanycapframe.pas, source/ccparallelcapframe.lfm (inherits from ccManyCapFrame.lfm)
Inputs:
- Up to 8 individual capacitance values (C1 to C8) [Code variables: FEditArray - an array of TEdit in TManyCapFrame]
- Important: All input capacitance values should be in the same units. The application displays a reminder "Same units!".
Outputs:
- Total capacitance (C) [Code variable: capa in TManyCapFrame]
- The number of decimal places for the output can be adjusted using an up/down control.
Formula: The total capacitance $C_{total}$ for $n$ capacitors connected in parallel is calculated as the direct sum of the individual capacitances: $$C_{total} = \sum_{i=1}^{n} C_i$$
Validation (TManyCapFrame.ValidData): Any non-empty input fields must contain positive numbers.
Real-World Idea: Calculating the total capacitance of multiple components connected across the same two nodes in a circuit, or analyzing charge sharing in switching circuits.

Semiconductor p/n Junction Capacitance

Real-World Applications and Problem Solving Ideas

CapaCalc can be a useful tool for students, engineers, and researchers working with electrical circuits and semiconductor devices. By providing specific calculation models, it serves as a useful educational tool and a practical utility in various fields of electrical engineering and physics. Here are some ideas on how the different calculation types can be applied:

Compilation

The application is distributed as Pascal source code only. It can be compiled with Lazarus v2.0+/FPC3.0+ (or potentially older versions, though not explicitly tested). No third-party components are needed.

Tested on Windows 32bit/64 bit and Linux 64 bit, but it should work also on other platforms supported by Lazarus.

To compile:

Ensure you have Lazarus IDE and Free Pascal Compiler installed.
Open the source/CapaCalc.lpr project file in Lazarus.
Build the project (Run -> Build All Project Files or press Shift+F9).
The executable will be generated in the project directory.

Core Units and String Resources

This section describes the units (ccGlobal.pas) and string resources (ccStrings.pas) used throughout the application, which are fundamental to its operation and extensibility.

`ccGlobal.pas`: Physical Constants and Unit Factors

This unit defines fundamental physical constants, enumeration types for various units, and conversion factors used to handle calculations across different unit systems.

All calculations within the application are performed using Standard International (SI) units (meters, Farads, Volts per meter, per cubic meter, etc.). Input values are converted from the user-selected units to their corresponding SI values upon reading, and calculated results are converted back to user-selected units for display in the UI.

Key Physical Constants Defined:

eps0 = 8.854187817E-12; (Permittivity of free space in Farads per meter)
q = 1.60217733E-19; (Elementary charge in Coulombs)
kB = 1.380658E-23; (Boltzmann constant in Joules per Kelvin)
Pi = 3.1415926535897932384626; (Mathematical constant Pi)
TwoPi = 6.2831853071795864769253; (Mathematical constant Two times Pi)

Unit Enumeration Types:

Enums are used to represent the different available units for various physical quantities:

TLenUnits = (lu_nm, lu_Microns, lu_cm, lu_m); (Length units: nanometers, micrometers, centimeters, meters)
TAreaUnits = (au_nm2, au_Microns2, au_cm2, au_m2); (Area units: square nanometers, square micrometers, square centimeters, square meters)
TVolumeUnits = (vu_nm3, vu_Microns3, vu_cm3, vu_m3); (Volume units: cubic nanometers, cubic micrometers, cubic centimeters, cubic meters)
TCapaUnits = (cu_aF, cu_fF, cu_pF, cu_nF, cu_F); (Capacitance units: attoFarads, femtoFarads, picoFarads, nanoFarads, Farads)
TEFieldUnits = (eu_mV_nm, eu_V_micron, eu_kV_cm, eu_MV_m, eu_V_m); (Electric Field units: millivolts per nanometer, Volts per micrometer, kilovolts per centimeter, Megavolts per meter, Volts per meter)
TTempUnits = (tuK, tuC); (Temperature units: Kelvin, Celsius)
TMaterial = (mSi, mGaAs, mGe, mInP); (Semiconductor materials: Silicon, Gallium Arsenide, Germanium, Indium Phosphide)

Unit Conversion Factor Arrays:

Arrays indexed by the unit enumeration types store the conversion factor from that unit to the corresponding SI unit.

LenFactor : array[TLenUnits] of double = ( 1E-9, 1E-6, 1E-2, 1.0);
AreaFactor : array[TAreaUnits] of double = ( 1E-18, 1E-12, 1E-4, 1.0);
VolumeFactor : array[TVolumeUnits] of double = ( 1E-27, 1E-18, 1E-6, 1.0);
CapaFactor : array[TCapaUnits] of double = ( 1E-18, 1E-15, 1E-12, 1E-9, 1.0 );
EFieldFactor : array[TEFieldUnits] of double = ( 1E-3/1E-9, 1.0/1E-6, 1E3/1E-2, 1E6/1, 1.0 );

Example of Unit Conversion in Code:

Input values are read as strings, converted to Extended (double), and then multiplied by the appropriate factor based on the selected unit's item index in the corresponding TComboBox.

pascal

// Reading and converting an input length value from a TEdit and TComboBox
var
  L_input_value: Extended; // Value read from edit field
  L_si: Extended; // Value in SI units (meters)
  LengthUnitsIndex: Integer; // Index from the units combobox

LengthUnitsIndex := CbLengthUnits.ItemIndex; // Get selected unit index
TryStrToFloat(EdLength.Text, L_input_value); // Read value from edit field
L_si := L_input_value * LenFactor[TLenUnits(LengthUnitsIndex)]; // Convert to meters

Output values, calculated in SI units, are converted back to the desired display units by dividing by the appropriate factor before formatting.

pascal

// Converting a calculated capacitance value from SI (Farads) to display units
var
  capa_si: Extended; // Calculated capacitance in Farads
  capa_display: Extended; // Capacitance in display units
  CapaUnitsIndex: Integer; // Index from the units combobox

// ... capa_si is calculated ...

CapaUnitsIndex := CbCapaUnits.ItemIndex; // Get selected unit index
capa_display := capa_si / CapaFactor[TCapaUnits(CapaUnitsIndex)]; // Convert to display units
TxtCapa.Text := FormatFloat(CapaStdFormat, capa_display); // Format and display

Semiconductor Material Properties:

MaterialEps : array [TMaterial] of double: Stores the relative permittivity ($\epsilon_r$) multiplied by $\epsilon_0$ for supported materials, giving $\epsilon_s$ in F/m.
ni : array [TMaterial] of double: Stores the intrinsic carrier concentration ($n_i$) in 1/cm³ for supported materials at 300K.

Format Strings: Standard format strings for displaying numbers in results fields:

CapaExpFormat = '0.000E+00'; (Scientific notation)
CapaStdFormat = '0.000'; (Standard decimal format)
CapaPerAreaFormat = '0.000E+00';
CapaPerLengthFormat = '0.000E+00';
ConcFormat = '0.00E+00'; (Format for concentrations)
LenStdFormat = '0.00'; (Standard decimal format for length/width/height/distance)
AreaStdFormat = '0.00E+00'; (Format for area)

`ccStrings.pas`: String Resources

This unit contains resourcestring definitions for all user-facing text elements within the application's GUI and message dialogs. This includes labels for input fields, captions for tabs and buttons, error messages, and informational text (like accuracy notes). Centralizing these strings simplifies text management and is a key practice for software internationalization (although only English strings are currently provided).

Example resourcestring definitions:

pascal

resourcestring
  SAccuracy2Percent = 'Accuracy ca. 2%';
  SInputRequired = 'Input required.';
  SNumberRequired = 'Number required in this field.';
  SPositiveNumberRequired = 'Positive number required.';
  SRadiusNotLargerThanHalfDistance = 'Radius cannot be larger than half-distance.';
  SSphereRadiiMustNotBeEqual = 'The sphere radii must not be equal.';
  STemperatureDependenceNotSupported = 'Temperature dependence of this material not supported.';
  STemperaturePositive = 'Temperature in Kelvin must be a positive number.';
  SVoltageMustBeSmallerThanBuiltIn = 'The applied voltage must be smaller then the built-in voltage (%f V)';
  SParameterError = 'Parameter error';
  // ... and many others for labels and captions

Extending CapaCalc

Developers interested in adding new capacitance calculations or improving existing ones can contribute to the CapaCalc project. The modular structure, based on TBaseFrame descendants, makes it relatively straightforward to add new calculation types.

License

MIT License

Attributions

Compiler: Free Pascal (https://www.freepascal.org//
Integrated development environment: Lazarus (https://www.lazarus-ide.org//
Most of the README.md file was written by an AI prototype developed by Joao Schuler using Gemini 2.5 Flash.

Live chat for Free Pascal, Lazarus, Delphi and every Pascal programmer.

CCapaCalc

Member rating

README

CapaCalc

Introduction

Supported Capacitance Calculations

Parallel Plate Capacitor

Spherical Capacitor

Cylindrical Capacitor

Capacitance between Rectangular Conductor and Conducting Plane

Capacitance between Cylindrical Conductor and Conducting Plane

Capacitance between Two Cylinders

Capacitors in Series

Capacitors in Parallel

Semiconductor p/n Junction Capacitance

Real-World Applications and Problem Solving Ideas

Compilation

Core Units and String Resources

ccGlobal.pas: Physical Constants and Unit Factors

ccStrings.pas: String Resources

Extending CapaCalc

License

Attributions

CapaCalc

`ccGlobal.pas`: Physical Constants and Unit Factors

`ccStrings.pas`: String Resources