Functions

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• Functions by category
  • E series values
  • Two-gate circuit calculations
    • Two gate circuits operational characteristics
      • Formal AC equivalent circuits
        • Voltage gain
        • Input impedance
        • Output impedance
        • Current gain
        • Voltage gain, input impedance, output impedance, and current gain
      • Physical AC equivalent circuits
    • Two-gate parameter sets for special circuits
    • Two-gate parameter set conversions
      • Conversion between H, Z, Y, K, and A parameters
      • H parameter set conversion for common emitter, common collector, and common base circuits
  • Coupling capacitors, emitter capacitors
  • Tool functions
    • Parallel impedances
    • Rounding
    • Tolerances
    • Ratio to dB and vice versa conversions
• Functions reference
  • a_params_current_gain
  • a_params_input_impedance
  • a_params_op_characteristics
  • a_params_output_impedance
  • a_params_to_h
  • a_params_to_k
  • a_params_to_y
  • a_params_to_z
  • a_params_voltage_gain
  • coupling_capacitor
  • dB_to_ratio
  • emitter_capacitor
  • E12_value
  • E12_value_up
  • E192_value
  • E192_value_up
  • E24_value
  • E24_value_up
  • E3_value
  • E3_value_up
  • E48_value
  • E48_value_up
  • E6_value
  • E6_value_up
  • E96_value
  • E96_value_up
  • h_params_cb_to_cc
  • h_params_cb_to_ce
  • h_params_cc_to_cb
  • h_params_cc_to_ce
  • h_params_ce_to_cb
  • h_params_ce_to_cc
  • h_params_current_gain
  • h_params_input_impedance
  • h_params_op_characteristics
  • h_params_output_impedance
  • h_params_to_a
  • h_params_to_k
  • h_params_to_y
  • h_params_to_z
  • h_params_voltage_gain
  • increase_for_tolerance
  • k_params_to_a
  • k_params_to_h
  • k_params_to_y
  • k_params_to_z
  • parallel_impedance
  • phys_params_current_gain
  • phys_params_input_impedance
  • phys_params_op_characteristics
  • phys_params_output_impedance
  • phys_params_voltage_gain
  • power_dB_to_ratio
  • power_ratio_to_dB
  • ratio_to_dB
  • round_leading_digits
  • y_params_current_gain
  • y_params_input_impedance
  • y_params_op_characteristics
  • y_params_output_impedance
  • y_params_resistor_horizontal
  • y_params_to_a
  • y_params_to_h
  • y_params_to_k
  • y_params_to_z
  • y_params_voltage_gain
  • z_params_current_gain
  • z_params_input_impedance
  • z_params_op_characteristics
  • z_params_output_impedance
  • z_params_resistor_vertical
  • z_params_to_a
  • z_params_to_h
  • z_params_to_k
  • z_params_to_y
  • z_params_voltage_gain
• Literature and information sources

Functions by category

E series values

E3_value

Choose value from E3 series closest to a given value.
 

E6_value

Choose value from E6 series closest to a given value.
 

E12_value

Choose value from E12 series closest to a given value.
 

E24_value

Choose value from E24 series closest to a given value.
 

E48_value

Choose value from E48 series closest to a given value.
 

E96_value

Choose value from E96 series closest to a given value.
 

E192_value

Choose value from E192 series closest to a given value.
 

Two-gate circuit calculations

Two gate circuits operational characteristics

$$\begin{array}{ccccccc}{\underset{¯}{v}}_u& =& \frac{{\underset{¯}{U}}_2}{{\underset{¯}{U}}_1}& \text{Voltage gain ratio}& & v_u& \text{in real numbers calculations}\\ {\underset{¯}{z}}_{\text{i}}& =& \frac{{\underset{¯}{U}}_1}{{\underset{¯}{I}}_1}& \text{Input impedance}& & r_{\text{i}}& \text{in real numbers calculations}\\ {\underset{¯}{z}}_{\text{o}}& =& -\frac{\underset{{\underset{¯}{Z}}_{\text{L}}\to \mathrm{\infty }}{lim}{\underset{¯}{U}}_2}{{{\underset{¯}{I}}_2|}_{{\underset{¯}{Z}}_{\text{L}}=0}}& \text{Output impedance}& & r_{\text{o}}& \text{in real numbers calculations}\\ {\underset{¯}{v}}_i& =& \frac{{\underset{¯}{I}}_2}{{\underset{¯}{I}}_1}& \text{Current gain ratio}& & v_i& \text{in real numbers calculations}\end{array}$$

 

Formal AC equivalent circuits

Voltage gain

h_params_voltage_gain

Calculate voltage gain for two-gate circuit specified by H parameter set and load resistor.
 

z_params_voltage_gain

Calculate voltage gain for two-gate circuit specified by Z parameter set and load resistor.
 

y_params_voltage_gain

Calculate voltage gain for two-gate circuit specified by Y parameter set and load resistor.
 

a_params_voltage_gain

Calculate voltage gain for two-gate circuit specified by A parameter set and load resistor.
 

Input impedance

h_params_input_impedance

Calculate input impedance for two-gate circuit specified by H parameter set and load resistor.
 

z_params_input_impedance

Calculate input impedance for two-gate circuit specified by Z parameter set and load resistor.
 

y_params_input_impedance

Calculate input impedance for two-gate circuit specified by Y parameter set and load resistor.
 

a_params_input_impedance

Calculate input impedance for two-gate circuit specified by A parameter set and load resistor.
 

Output impedance

h_params_output_impedance

Calculate output impedance for two-gate circuit specified by H parameter set and generator impedance.
 

z_params_output_impedance

Calculate output impedance for two-gate circuit specified by Z parameter set and generator impedance.
 

y_params_output_impedance

Calculate output impedance for two-gate circuit specified by Y parameter set and generator impedance.
 

a_params_output_impedance

Calculate output impedance for two-gate circuit specified by A parameter set and generator impedance.
 

Current gain

h_params_current_gain

Calculate current gain for two-gate circuit specified by H parameter set and load resistor.
 

z_params_current_gain

Calculate current gain for two-gate circuit specified by Z parameter set and load resistor.
 

y_params_current_gain

Calculate current gain for two-gate circuit specified by Y parameter set and load resistor.
 

a_params_current_gain

Calculate current gain for two-gate circuit specified by A parameter set and load resistor.
 

Voltage gain, input impedance, output impedance, and current gain

h_params_op_characteristics

Calculate operational characteristics for two-gate circuit specified by H parameter set, generator impedance, and load resistor.
 

z_params_op_characteristics

Calculate operational characteristics for two-gate circuit specified by Z parameter set, generator impedance, and load resistor.
 

y_params_op_characteristics

Calculate operational characteristics for two-gate circuit specified by Y parameter set, generator impedance, and load resistor.
 

a_params_op_characteristics

Calculate operational characteristics for two-gate circuit specified by A parameter set, generator impedance, and load resistor.
 

Physical AC equivalent circuits

Common emitter circuit, no negative AC feedback.

$$\begin{array}{ccc}{v}_u& =& -\frac{\beta R_{\text{L}}}{r_{\text{be}}}\\ r_{\text{i}}& =& r_{\text{be}}\\ r_{\text{o}}& =& r_{\text{ce}}\\ v_i& =& \beta \end{array}$$

 

phys_params_voltage_gain

Calculate voltage gain for two-gate circuit specified by physical parameter set for common emitter circuit and load resistor.
 

phys_params_input_impedance

Calculate input impedance for two-gate circuit specified by physical parameter set for common emitter circuit and load resistor.
 

phys_params_output_impedance

Calculate output impedance for two-gate circuit specified by physical parameter set for common emitter circuit and generator impedance.
 

phys_params_current_gain

Calculate current gain for two-gate circuit specified by physical parameter set for common emitter circuit and load resistor.
 

phys_params_op_characteristics

Calculate voltage gain, input impedance, output impedance, and current gain for two-gate circuit specified by physical parameter set for common emitter circuit, generator impedance, and load resistor.

Two-gate parameter sets for special circuits

y_params_resistor_horizontal

Create Y parameter set matrix for horizontal resistor.
 

z_params_resistor_vertical

Create Z parameter set matrix for vertical resistor.
 

Two-gate parameter set conversions

Conversion between H, Z, Y, K, and A parameters

The following function convert a two-gate circuits parameter set into another parameter set:

Function	Conversion
h_params_to_z	H → Z
h_params_to_y	H → Y
h_params_to_a	H → A
h_params_to_k	H → K
z_params_to_h	Z → H
z_params_to_y	Z → Y
z_params_to_a	Z → A
z_params_to_k	Z → K
y_params_to_h	Y → H
y_params_to_z	Y → Z
y_params_to_a	Y → A
y_params_to_k	Y → K
a_params_to_h	A → H
a_params_to_z	A → Z
a_params_to_y	A → Y
a_params_to_k	A → K
k_params_to_h	K → H
k_params_to_z	K → Z
k_params_to_y	K → Y
k_params_to_a	K → A

H parameter set conversion for common emitter, common collector, and common base circuits

The following functions convert a H parameter set for one common transistor port into a H parameter set for another common transistor port:

Function	Conversion
h_params_ce_to_cc	Common emitter → Common collector
h_params_ce_to_cb	Common emitter → Common base
h_params_cc_to_ce	Common collector → Common emitter
h_params_cc_to_cb	Common collector → Common base
h_params_cb_to_ce	Common base → Common emitter
h_params_cb_to_cc	Common base → Common collector

Coupling capacitors, emitter capacitors

coupling_capacitor

Calculate a coupling capacitor for given output impedance, input impedance, cut-off frequency, and maximum attenuation.
 

emitter_capacitor

Calculate emitter capacitor (capacitor parallel to resistor at emitter in common emitter circuit).
 

Tool functions

Parallel impedances

parallel_impedance

Calculate resulting impedance of a parallel circuit of impedances.
 

Rounding

round_leading_digits

Round numeric values, keep specified number of leading digits.
 

Tolerances

increase_for_tolerance

Increase a given value so applying a tolerance to the new nominal value does not fall below the given value.
 

Ratio to dB and vice versa conversions

ratio_to_dB

Calculate dB value for voltage or current gain ratio.
 

power_ratio_to_dB

Calculate dB value for power gain ratio.
 

power_dB_to_ratio

Calculate power gain ratio for dB value.
 

dB_to_ratio

Calculate voltage or current gain ratio for dB value.

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Functions reference

a_params_current_gain

Calculate current gain for two-gate circuit and load resistor.

[vi] = a_params_current_gain(a, rl);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vi	scalar/vector/matrix same size as rl	Current gain ratio

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a_params_input_impedance

Calculate input impedance for two-gate circuit and load resistor.

[ri] = a_params_input_impedance(a, rl);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
ri	scalar/vector/matrix same size as rl	Input impedance

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a_params_op_characteristics

Calculate operational characteristics for two-gate circuit, generator impedance, and load resistor.

$$\begin{array}{ccc}\left(\begin{array}{c}{\underset{¯}{u}}_1\\ {\underset{¯}{i}}_1\end{array}\right)& =& \left(\begin{array}{cc}{\underset{¯}{a}}_{11}& {\underset{¯}{a}}_{12}\\ {\underset{¯}{a}}_{21}& {\underset{¯}{a}}_{22}\end{array}\right)\left(\begin{array}{c}{\underset{¯}{u}}_2\\ -{\underset{¯}{i}}_2\end{array}\right)\\ & & \\ {\underset{¯}{v}}_u& =& \frac{{\underset{¯}{Z}}_{\text{L}}}{{\underset{¯}{a}}_{11}{\underset{¯}{Z}}_{\text{L}}+{\underset{¯}{a}}_{12}}\\ {\underset{¯}{z}}_{\text{i}}& =& \frac{{\underset{¯}{a}}_{11}{\underset{¯}{Z}}_{\text{L}}+{\underset{¯}{a}}_{12}}{{\underset{¯}{a}}_{21}{\underset{¯}{Z}}_{\text{L}}+{\underset{¯}{a}}_{22}}\\ {\underset{¯}{z}}_{\text{o}}& =& \frac{{\underset{¯}{a}}_{22}{\underset{¯}{Z}}_{\text{G}}+{\underset{¯}{a}}_{12}}{{\underset{¯}{a}}_{21}{\underset{¯}{Z}}_{\text{G}}+{\underset{¯}{a}}_{11}}\\ {\underset{¯}{v}}_i& =& -\frac{1}{{\underset{¯}{a}}_{21}{\underset{¯}{Z}}_{\text{L}}+{\underset{¯}{a}}_{22}}\end{array}$$

 

[vu, ri, ro, vi] = a_params_op_characteristics(a, rg, rl);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix
rg	scalar/vector/matrix	Generator impedance
rl	scalar/vector/matrix	Load resistor

If both rg and rl are specified as vector or matrix, they must have the same size.

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rg / rl	Voltage gain ratio
ri	scalar/vector/matrix same size as rg / rl	Input impedance
ro	scalar/vector/matrix same size as rg / rl	Output impedance
vi	scalar/vector/matrix same size as rg / rl	Current gain ratio

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a_params_output_impedance

Calculate output impedance for two-gate circuit and generator impedance.

[ro] = a_params_output_impedance(a, rg);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix
rg	scalar/vector/matrix	Generator impedance

Result list

Name	Type	Purpose
ro	scalar/vector/matrix same size as rg	Output impedance

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a_params_to_h

Convert A parameter set matrix to H parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11}& {\underset{¯}{h}}_{12}\\ {\underset{¯}{h}}_{21}& {\underset{¯}{h}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{a}}_{22}}·\left(\begin{array}{cc}{\underset{¯}{a}}_{12}& \det \underset{¯}{a}\\ -1& {\underset{¯}{a}}_{21}\end{array}\right)$$

 

[h] = a_params_to_h(a);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

Result list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

---

a_params_to_k

Convert A parameter set matrix to K parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{k}}_{11}& {\underset{¯}{k}}_{12}\\ {\underset{¯}{k}}_{21}& {\underset{¯}{k}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{a}}_{11}}·\left(\begin{array}{cc}{\underset{¯}{a}}_{21}& -\det \underset{¯}{a}\\ -1& {\underset{¯}{a}}_{12}\end{array}\right)$$

 

[k] = a_params_to_k(a);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

Result list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

---

a_params_to_y

Convert A parameter set matrix to Y parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{y}}_{11}& {\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{a}}_{12}}·\left(\begin{array}{cc}{\underset{¯}{a}}_{22}& -\det \underset{¯}{a}\\ -1& {\underset{¯}{a}}_{11}\end{array}\right)$$

 

[y] = a_params_to_y(a);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

Result list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

---

a_params_to_z

Convert A parameter set matrix to Z parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{z}}_{11}& {\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{a}}_{21}}·\left(\begin{array}{cc}{\underset{¯}{a}}_{11}& \det \underset{¯}{a}\\ 1& {\underset{¯}{a}}_{22}\end{array}\right)$$

 

[z] = a_params_to_z(a);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

Result list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

---

a_params_voltage_gain

Calculate voltage gain for two-gate circuit and load resistor.

[vu] = a_params_voltage_gain(a, rl);

Argument list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rl	Voltage gain ratio

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coupling_capacitor

Calculate coupling capacitor to connect

• a source to an amplifier,
• an amplifier stage to the next stage, or
• an amplifier output to a load resistor.

[c] = coupling_capacitor(rout, rin, f, a);

$$\begin{array}{ccccc}{C}_{\text{K,3dB}}& =& \frac{1}{2\mathrm{\pi }f(R_{\text{out}}+R_{\text{in}})}& & \text{3 dB attenuation at given frequency}\\ C_{\text{K}}& =& \frac{C_{\text{K,3db}}}{\sqrt{{10}^{a/10\text{dB}}-1}}& & \text{Specified attenuation at given frequency}\end{array}$$

Argument list

Name	Type	Purpose
rout	scalar/vector/matrix	Ouput impedance in Ohms (impedance of source, previous stage, or amplifier)
rin	scalar/vector/matrix	Input impedance in Ohms (impedance of amplifier, next stage, or load resistor)
f	scalar/vector/matrix	Cut-off frequency in Hertz
a	scalar/vector/matrix	Optional parameter: Allowed attenuation (positive value in dB) at given cut-off frequency. Optional parameter, default: 3dB

Result list

Name	Type	Purpose
c	scalar/vector/matrix	Minimum required capacitor in Farad.

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dB_to_ratio

Calculate voltage or current gain ratio for given dB value.

$$\begin{array}{ccc}{v}_u& =& {10}^{v_{u,\text{dB}}/\mathrm{20}\text{dB}}\\ v_i& =& {10}^{v_{i,\text{dB}}/\mathrm{20}\text{dB}}\end{array}$$

 

[gainratio] = dB_to_ratio(gaindb);

Argument list

Name	Type	Purpose
gaindb	scalar/vector/matrix	dB value for voltage or current gain

Result list

Name	Type	Purpose
gainratio	scalar/vector/matrix same size as gaindb	Voltage or current gain ratio

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emitter_capacitor

Calculate capacitor value to place parallel to the resistor connected to emitter in common emitter circuit.

[c] = emitter_capacitor(rg, rbe, re, beta, f, a);

$$\begin{array}{ccccc}{C}_{\text{E,3dB}}& =& \frac{R_{\text{G}}+r_{\text{be}}+\beta R_{\text{E}}}{2\mathrm{\pi }f{R}_{\text{E}}(R_{\text{G}}+r_{\text{be}})}& & \text{3 dB attenuation at given frequency}\\ C_{\text{E}}& =& \frac{C_{\text{E,3db}}}{\sqrt{{10}^{a/10\text{dB}}-1}}& & \text{Specified attenuation at given frequency}\end{array}$$

Argument list

Name	Type	Purpose
rg	scalar/vector/matrix	Generator impedance in Ohms.
rbe	scalar/vector/matrix	Transistors base to emitter AC impedance in Ohms.
re	scalar/vector/matrix	Resistor connected to emitter in Ohms.
beta	scalar/vector/matrix	Transistor AC short-circuit current gain (the h_f parameter).
f	scalar/vector/matrix	Cut-off frequency in Hertz.
a	scalar/vector/matrix	Maximum allowed attenuation at specified cut-off frequency, positive value in dB. Optional parameter, default: 3 dB.

Result list

Name	Type	Purpose
c	scalar/vector/matrix	Required minimum capacitor value in Farad.

If rg, rbe, re, beta, f, and/or a are non-scalar values, sizes must match.

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E12_value

Choose E12 series value next to a given value.

The values in the E12 series are power-of-ten multiples of the following coefficients:

  1.0  1.2  1.5  1.8  2.2  2.7  3.3  3.9  4.7  5.6  6.8  8.2

[r] = E12_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E12 series next to x

---

E12_value_up

Choose E12 series value for a given value, round upwards.

[r] = E12_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E12 series value not less than x

---

E192_value

Choose E192 series value next to a given value.

The values in the E192 series are power-of-ten multiples of the following coefficients:

  1.00  1.01  1.02  1.04  1.05  1.06  1.07  1.09
  1.10  1.11  1.13  1.14  1.15  1.17  1.18  1.20
  1.21  1.23  1.24  1.26  1.27  1.29  1.30  1.32
  1.33  1.35  1.37  1.38  1.40  1.42  1.43  1.45
  1.47  1.49  1.50  1.52  1.54  1.56  1.58  1.60
  1.62  1.64  1.65  1.67  1.69  1.72  1.74  1.76
  1.78  1.80  1.82  1.84  1.87  1.89  1.91  1.93
  1.96  1.98  2.00  2.03  2.05  2.08  2.10  2.13
  2.15  2.18  2.21  2.23  2.26  2.29  2.32  2.34
  2.37  2.40  2.43  2.46  2.49  2.52  2.55  2.58
  2.61  2.64  2.67  2.71  2.74  2.77  2.80  2.84
  2.87  2.91  2.94  2.98  3.01  3.05  3.09  3.12
  3.16  3.20  3.24  3.28  3.32  3.36  3.40  3.44
  3.48  3.52  3.57  3.61  3.65  3.70  3.74  3.79
  3.83  3.88  3.92  3.97  4.02  4.07  4.12  4.17
  4.22  4.27  4.32  4.37  4.42  4.48  4.53  4.59
  4.64  4.70  4.75  4.81  4.87  4.93  4.99  5.05
  5.11  5.17  5.23  5.30  5.36  5.42  5.49  5.56
  5.62  5.69  5.76  5.83  5.90  5.97  6.04  6.12
  6.19  6.26  6.34  6.42  6.49  6.57  6.65  6.73
  6.81  6.90  6.98  7.06  7.15  7.23  7.32  7.41
  7.50  7.59  7.68  7.77  7.87  7.96  8.06  8.16
  8.25  8.35  8.45  8.56  8.66  8.76  8.87  8.98
  9.09  9.20  9.31  9.42  9.53  9.65  9.76  9.88

[r] = E192_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E192 series next to x

---

E192_value_up

Choose E192 series value for a given value, round upwards.

[r] = E192_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E192 series value not less than x

---

E24_value

Choose E24 series value next to a given value.

The values in the E24 series are power-of-ten multiples of the following coefficients:

  1.0  1.1  1.2  1.3  1.5  1.6  1.8  2.0  2.2  2.4  2.7  3.0
  3.3  3.6  3.9  4.3  4.7  5.1  5.6  6.2  6.8  7.5  8.2  9.1

[r] = E24_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E24 series next to x

---

E24_value_up

Choose E24 series value for a given value, round upwards.

[r] = E24_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E24 series value not less than x

---

E3_value

Choose E3 series value next to a given value.

The values in the E3 series are power-of-ten multiples of the following coefficients:

  1.0  2.2  4.7

[r] = E3_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E3 series next to x

---

E3_value_up

Choose E3 series value for a given value, round upwards.

[r] = E3_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E3 series value not less than x

---

E48_value

Choose E48 series value next to a given value.

The values in the E48 series are power-of-ten multiples of the following coefficients:

  1.00  1.05  1.10  1.15  1.21  1.27  1.33  1.40
  1.47  1.54  1.62  1.69  1.78  1.87  1.96  2.05
  2.15  2.26  2.37  2.49  2.61  2.74  2.87  3.01
  3.16  3.32  3.48  3.65  3.83  4.02  4.22  4.42
  4.64  4.87  5.11  5.36  5.62  5.90  6.19  6.49
  6.81  7.15  7.50  7.87  8.25  8.66  9.09  9.53

[r] = E48_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E48 series next to x

---

E48_value_up

Choose E48 series value for a given value, round upwards.

[r] = E48_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E48 series value not less than x

---

E6_value

Choose E6 series value next to a given value.

The values in the E6 series are power-of-ten multiples of the following coefficients:

  1.0  1.5  2.2  3.3  4.7  6.8

[r] = E6_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E6 series next to x

---

E6_value_up

Choose E6 series value for a given value, round upwards.

[r] = E6_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E6 series value not less than x

---

E96_value

Choose E96 series value next to a given value.

The values in the E96 series are power-of-ten multiples of the following coefficients:

  1.00  1.02  1.05  1.07  1.10  1.13  1.15  1.18
  1.21  1.24  1.27  1.30  1.33  1.37  1.40  1.43
  1.47  1.50  1.54  1.58  1.62  1.65  1.69  1.74
  1.78  1.82  1.87  1.91  1.96  2.00  2.05  2.10
  2.15  2.21  2.26  2.32  2.37  2.43  2.49  2.55
  2.61  2.67  2.74  2.80  2.87  2.94  3.01  3.09
  3.16  3.24  3.32  3.40  3.48  3.57  3.65  3.74
  3.83  3.92  4.02  4.12  4.22  4.32  4.42  4.53
  4.64  4.75  4.87  4.99  5.11  5.23  5.36  5.49
  5.62  5.76  5.90  6.04  6.19  6.34  6.49  6.56
  6.81  6.98  7.15  7.32  7.50  7.68  7.87  8.06
  8.25  8.45  8.66  8.87  9.09  9.31  9.53  9.76

[r] = E96_value(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Value from E96 series next to x

---

E96_value_up

Choose E96 series value for a given value, round upwards.

[r] = E96_value_up(x);

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Given resistor or capacitor value

Result list

Name	Type	Purpose
r	scalar/vector/matrix same size as x	Next E96 series value not less than x

---

h_params_cb_to_cc

Convert H parameter set matrix for common base circuit to H parameter set matrix for common collector circuit.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{c}}& {\underset{¯}{h}}_{12\text{c}}\\ {\underset{¯}{h}}_{21\text{c}}& {\underset{¯}{h}}_{22\text{c}}\end{array}\right)=\frac{1}{1-{\underset{¯}{h}}_{12\text{b}}+{\underset{¯}{h}}_{21\text{b}}+\det {\underset{¯}{h}}_{\text{b}}}·\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{b}}& {\underset{¯}{h}}_{21\text{b}}+1\\ {\underset{¯}{h}}_{12\text{b}}-1& {\underset{¯}{h}}_{22\text{b}}\end{array}\right)$$

 

[hcc] = h_params_cb_to_cc(hcb);

Argument list

Name	Type	Purpose
hcb	2×2 matrix	H parameter set for common base cirucit

Result list

Name	Type	Purpose
hcc	2×2 matrix	H parameter set for common collector cirucit

---

h_params_cb_to_ce

Convert H parameter set matrix for common base circuit to H parameter set matrix for common emitter circuit.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{e}}& {\underset{¯}{h}}_{12\text{e}}\\ {\underset{¯}{h}}_{21\text{e}}& {\underset{¯}{h}}_{22\text{e}}\end{array}\right)=\frac{1}{1-{\underset{¯}{h}}_{12\text{b}}+{\underset{¯}{h}}_{21\text{b}}+\det {\underset{¯}{h}}_{\text{b}}}·\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{b}}& -({\underset{¯}{h}}_{12\text{b}}-\det {\underset{¯}{h}}_{\text{b}})\\ -({\underset{¯}{h}}_{21\text{b}}+\det {\underset{¯}{h}}_{\text{b}})& {\underset{¯}{h}}_{22\text{b}}\end{array}\right)$$

 

[hce] = h_params_cb_to_ce(hcb);

Argument list

Name	Type	Purpose
hcb	2×2 matrix	H parameter set for common base cirucit

Result list

Name	Type	Purpose
hce	2×2 matrix	H parameter set for common emitter cirucit

---

h_params_cc_to_cb

Convert H parameter set matrix for common collector circuit to H parameter set matrix for common base circuit.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{b}}& {\underset{¯}{h}}_{12\text{b}}\\ {\underset{¯}{h}}_{21\text{b}}& {\underset{¯}{h}}_{22\text{b}}\end{array}\right)=\frac{1}{\det {\underset{¯}{h}}_{\text{c}}}·\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{c}}& {\underset{¯}{h}}_{21\text{c}}+\det {\underset{¯}{h}}_{\text{c}}\\ {\underset{¯}{h}}_{12\text{c}}-\det {\underset{¯}{h}}_{\text{c}}& {\underset{¯}{h}}_{22\text{c}}\end{array}\right)$$

 

[hcb] = h_params_cc_to_cb(hcc);

Argument list

Name	Type	Purpose
hcc	2×2 matrix	H parameter set for common collector cirucit

Result list

Name	Type	Purpose
hcb	2×2 matrix	H parameter set for common base cirucit

---

h_params_cc_to_ce

Convert H parameter set matrix for common collector circuit to H parameter set matrix for common emitter circuit.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{e}}& {\underset{¯}{h}}_{12\text{e}}\\ {\underset{¯}{h}}_{21\text{e}}& {\underset{¯}{h}}_{22\text{e}}\end{array}\right)=\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{c}}& 1-{\underset{¯}{h}}_{12\text{c}}\\ -1-{\underset{¯}{h}}_{21\text{c}}& {\underset{¯}{h}}_{22\text{c}}\end{array}\right)$$

 

[hce] = h_params_cc_to_ce(hcc);

Argument list

Name	Type	Purpose
hcc	2×2 matrix	H parameter set for common collector cirucit

Result list

Name	Type	Purpose
hce	2×2 matrix	H parameter set for common emitter cirucit

---

h_params_ce_to_cb

Convert H parameter set matrix for common emitter circuit to H parameter set matrix for common base circuit.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{b}}& {\underset{¯}{h}}_{12\text{b}}\\ {\underset{¯}{h}}_{21\text{b}}& {\underset{¯}{h}}_{22\text{b}}\end{array}\right)=\frac{1}{1-{\underset{¯}{h}}_{12\text{e}}+{\underset{¯}{h}}_{21\text{e}}+\det {\underset{¯}{h}}_{\text{e}}}·\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{e}}& -({\underset{¯}{h}}_{12\text{e}}-\det {\underset{¯}{h}}_{\text{e}})\\ -({\underset{¯}{h}}_{21\text{e}}+\det {\underset{¯}{h}}_{\text{e}})& {\underset{¯}{h}}_{22\text{e}}\end{array}\right)$$

 

[hcb] = h_params_ce_to_cb(hce);

Argument list

Name	Type	Purpose
hce	2×2 matrix	H parameter set for common emitter cirucit

Result list

Name	Type	Purpose
hcb	2×2 matrix	H parameter set for common base cirucit

---

h_params_ce_to_cc

Convert H parameter set matrix for common emitter circuit to H parameter set matrix for common collector circuit.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{c}}& {\underset{¯}{h}}_{12\text{c}}\\ {\underset{¯}{h}}_{21\text{c}}& {\underset{¯}{h}}_{22\text{c}}\end{array}\right)=\left(\begin{array}{cc}{\underset{¯}{h}}_{11\text{e}}& 1-{\underset{¯}{h}}_{12\text{e}}\\ -1-{\underset{¯}{h}}_{21\text{e}}& {\underset{¯}{h}}_{22\text{e}}\end{array}\right)$$

 

[hcc] = h_params_ce_to_cc(hce);

Argument list

Name	Type	Purpose
hce	2×2 matrix	H parameter set for common emitter cirucit

Result list

Name	Type	Purpose
hcc	2×2 matrix	H parameter set for common collector cirucit

---

h_params_current_gain

Calculate current gain for two-gate circuit and load resistor.

[vi] = h_params_current_gain(h, rl);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vi	scalar/vector/matrix same size as rl	Current gain ratio

---

h_params_input_impedance

Calculate input impedance for two-gate circuit and load resistor.

[ri] = h_params_input_impedance(h, rl);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
ri	scalar/vector/matrix same size as rl	Input impedance

---

h_params_op_characteristics

Calculate operational characteristics for two-gate circuit, generator impedance, and load resistor.

$$\begin{array}{ccc}\left(\begin{array}{c}{\underset{¯}{u}}_1\\ {\underset{¯}{i}}_2\end{array}\right)& =& \left(\begin{array}{cc}{\underset{¯}{h}}_{11}& {\underset{¯}{h}}_{12}\\ {\underset{¯}{h}}_{21}& {\underset{¯}{h}}_{22}\end{array}\right)\left(\begin{array}{c}{\underset{¯}{i}}_1\\ {\underset{¯}{u}}_2\end{array}\right)\\ & & \\ {\underset{¯}{v}}_u& =& -\frac{{\underset{¯}{h}}_{21}{\underset{¯}{Z}}_{\text{L}}}{{\underset{¯}{Z}}_{\text{L}}\det \underset{¯}{h}+{\underset{¯}{h}}_{11}}& & \det \underset{¯}{h}& =& {\underset{¯}{h}}_{11}{\underset{¯}{h}}_{22}-{\underset{¯}{h}}_{12}{\underset{¯}{h}}_{21}\\ {\underset{¯}{z}}_{\text{i}}& =& \frac{{\underset{¯}{Z}}_{\text{L}}\det \underset{¯}{h}+{\underset{¯}{h}}_{11}}{{\underset{¯}{h}}_{22}{\underset{¯}{Z}}_{\text{L}}+1}\\ {\underset{¯}{z}}_{\text{o}}& =& \frac{{\underset{¯}{Z}}_{\text{G}}+{\underset{¯}{h}}_{11}}{{\underset{¯}{h}}_{22}{\underset{¯}{Z}}_{\text{G}}+\det \underset{¯}{h}}\\ {\underset{¯}{v}}_i& =& \frac{{\underset{¯}{h}}_{21}}{{\underset{¯}{h}}_{22}{\underset{¯}{Z}}_{\text{L}}+1}\end{array}$$

 

[vu, ri, ro, vi] = h_params_op_characteristics(h, rg, rl);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix
rg	scalar/vector/matrix	Generator impedance
rl	scalar/vector/matrix	Load resistor

If both rg and rl are specified as vector or matrix, they must have the same size.

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rg / rl	Voltage gain ratio
ri	scalar/vector/matrix same size as rg / rl	Input impedance
ro	scalar/vector/matrix same size as rg / rl	Output impedance
vi	scalar/vector/matrix same size as rg / rl	Current gain ratio

---

h_params_output_impedance

Calculate output impedance for two-gate circuit and generator impedance.

[ro] = h_params_output_impedance(h, rg);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix
rg	scalar/vector/matrix	Generator impedance

Result list

Name	Type	Purpose
ro	scalar/vector/matrix same size as rg	Output impedance

---

h_params_to_a

Convert H parameter set matrix to A parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{a}}_{11}& {\underset{¯}{a}}_{12}\\ {\underset{¯}{a}}_{21}& {\underset{¯}{a}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{h}}_{21}}·\left(\begin{array}{cc}-\det \underset{¯}{h}& -{\underset{¯}{h}}_{11}\\ -{\underset{¯}{h}}_{22}& -1\end{array}\right)$$

 

[a] = h_params_to_a(h);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

Result list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

---

h_params_to_k

Convert H parameter set matrix to K parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{k}}_{11}& {\underset{¯}{k}}_{12}\\ {\underset{¯}{k}}_{21}& {\underset{¯}{k}}_{22}\end{array}\right)=\frac{1}{\det \underset{¯}{h}}·\left(\begin{array}{cc}{\underset{¯}{h}}_{22}& -{\underset{¯}{h}}_{12}\\ -{\underset{¯}{h}}_{21}& {\underset{¯}{h}}_{11}\end{array}\right)$$

 

[k] = h_params_to_k(h);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

Result list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

---

h_params_to_y

Convert H parameter set matrix to Y parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{y}}_{11}& {\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{h}}_{11}}·\left(\begin{array}{cc}1& -{\underset{¯}{h}}_{12}\\ {\underset{¯}{h}}_{21}& \det \underset{¯}{h}\end{array}\right)$$

 

[y] = h_params_to_y(h);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

Result list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

---

h_params_to_z

Convert H parameter set matrix to Z parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{z}}_{11}& {\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{h}}_{22}}·\left(\begin{array}{cc}\det \underset{¯}{h}& {\underset{¯}{h}}_{12}\\ -{\underset{¯}{h}}_{21}& 1\end{array}\right)$$

 

[z] = h_params_to_z(h);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

Result list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

---

h_params_voltage_gain

Calculate voltage gain for two-gate circuit and load resistor.

[vu] = h_params_voltage_gain(h, rl);

Argument list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rl	Voltage gain ratio

---

increase_for_tolerance

[y] = increase_for_tolerance(x, tol);

Calculate y value for x, so y with applied tolerance tol does not fall below x.

Argument list

Name	Type	Purpose
x	scalar/vector/matrix	Minimum required values after applying tolerance
tol	scalar/vector/matrix	Tolerance in percent (0 to 100).

Result list

Name	Type	Purpose
y	scalar/vector/matrix same size as x and/or tol	Minimum nominal values, so applying the tolerance will not fall below x.

If both x and tol are non-scalar types, they must have same size.

---

k_params_to_a

Convert K parameter set matrix to A parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{a}}_{11}& {\underset{¯}{a}}_{12}\\ {\underset{¯}{a}}_{21}& {\underset{¯}{a}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{k}}_{21}}·\left(\begin{array}{cc}1& {\underset{¯}{k}}_{22}\\ {\underset{¯}{k}}_{11}& \det \underset{¯}{k}\end{array}\right)$$

 

[a] = k_params_to_a(k);

Argument list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

Result list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

---

k_params_to_h

Convert K parameter set matrix to H parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11}& {\underset{¯}{h}}_{12}\\ {\underset{¯}{h}}_{21}& {\underset{¯}{h}}_{22}\end{array}\right)=\frac{1}{\det \underset{¯}{k}}·\left(\begin{array}{cc}{\underset{¯}{k}}_{22}& -{\underset{¯}{k}}_{12}\\ -{\underset{¯}{k}}_{21}& {\underset{¯}{k}}_{11}\end{array}\right)$$

 

[h] = k_params_to_h(k);

Argument list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

Result list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

---

k_params_to_y

Convert K parameter set matrix to Y parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{y}}_{11}& {\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{k}}_{22}}·\left(\begin{array}{cc}\det \underset{¯}{k}& {\underset{¯}{k}}_{12}\\ -{\underset{¯}{k}}_{21}& 1\end{array}\right)$$

 

[y] = k_params_to_y(k);

Argument list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

Result list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

---

k_params_to_z

Convert K parameter set matrix to Z parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{z}}_{11}& {\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{k}}_{11}}·\left(\begin{array}{cc}1& -{\underset{¯}{k}}_{12}\\ {\underset{¯}{k}}_{21}& \det \underset{¯}{k}\end{array}\right)$$

 

[z] = k_params_to_z(k);

Argument list

Name	Type	Purpose
k	2×2 matrix	k parameter set matrix

Result list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

---

parallel_impedance

Calculate resulting impedance of multiple impedances in parallel circuit.

$${\underset{¯}{Z}}_{\text{par}}=\frac{1}{\frac{1}{{\underset{¯}{Z}}_1}+\frac{1}{{\underset{¯}{Z}}_2}+\cdots }$$

 

[rpar] = parallel_impedance(r1, ...);

Argument list

Name	Type	Purpose
r1	scalar/vector/matrix	First impedance value

If one or multiple arguments are specified as vector or matrix, sizes must match.

Result list

Name	Type	Purpose
rpar	scalar/vector/matrix Size depending on arguments	Resulting impedance of parallel circuit

---

phys_params_current_gain

Calculate current gain for two-gate circuit and load resistor.

[vi] = phys_params_current_gain(rbe, b, rce, rl);

Argument list

Name	Type	Purpose
rbe	scalar/vector/matrix	Base to emitter impedance of transistor (hi)
b	scalar/vector/matrix	Internal current gain of transistor (hf)
rce	scalar/vector/matrix	Collector to emitter impedance of transistor (1/ho)
rl	scalar/vector/matrix	Load resistor

If arguments are specified as vector/matrix, sizes must match for piecewise mathematical operations.

Result list

Name	Type	Purpose
vi	scalar/vector/matrix same size as rbe/b/rce/rl	Current gain ratio

---

phys_params_input_impedance

Calculate input impedance for two-gate circuit and load resistor.

[ri] = phys_params_input_impedance(rbe, b, rce, rl);

Argument list

Name	Type	Purpose
rbe	scalar/vector/matrix	Base to emitter impedance of transistor (hi)
b	scalar/vector/matrix	Internal current gain of transistor (hf)
rce	scalar/vector/matrix	Collector to emitter impedance of transistor (1/ho)
rl	scalar/vector/matrix	Load resistor

If arguments are specified as vector/matrix, sizes must match for piecewise mathematical operations.

Result list

Name	Type	Purpose
ri	scalar/vector/matrix same size as rbe/b/rce/rl	Input impedance

---

phys_params_op_characteristics

Calculate operational characteristics for two-gate circuit, generator impedance, and load resistor.

[vu, ri, ro, vi] = phys_params_op_characteristics(rbe, b, rce, rg, rl);

Argument list

Name	Type	Purpose
rbe	scalar/vector/matrix	Base to emitter impedance of transistor (hi)
b	scalar/vector/matrix	Internal current gain of transistor (hf)
rce	scalar/vector/matrix	Collector to emitter impedance of transistor (1/ho)
rg	scalar/vector/matrix	Generator impedance
rl	scalar/vector/matrix	Load resistor

If arguments are specified as vector/matrix, sizes must match for piecewise mathematical operations.

Result list

Name	Type	Purpose
vu	scalar/vector/matrix Size depends on sizes of rbe, b, rce, rg, and rl	Voltage gain ratio
ri	scalar/vector/matrix Size depends on sizes of rbe, b, rce, rg, and rl	Input impedance
ro	scalar/vector/matrix Size depends on sizes of rbe, b, rce, rg, and rl	Output impedance
vi	scalar/vector/matrix Size depends on sizes of rbe, b, rce, rg, and rl	Current gain ratio

---

phys_params_output_impedance

Calculate output impedance for two-gate circuit and generator impedance.

[ro] = phys_params_output_impedance(rbe, b, rce, rg);

Argument list

Name	Type	Purpose
rbe	scalar/vector/matrix	Base to emitter impedance of transistor (hi)
b	scalar/vector/matrix	Internal current gain of transistor (hf)
rce	scalar/vector/matrix	Collector to emitter impedance of transistor (1/ho)
rg	scalar/vector/matrix	Generator impedance

If arguments are specified as vector/matrix, sizes must match for piecewise mathematical operations.

Result list

Name	Type	Purpose
ro	scalar/vector/matrix same size as rbe/b/rce/rl	Output impedance

---

phys_params_voltage_gain

Calculate voltage gain for two-gate circuit and load resistor.

[vu] = phys_params_voltage_gain(rbe, b, rce, rl);

Argument list

Name	Type	Purpose
rbe	scalar/vector/matrix	Base to emitter impedance of transistor (hi)
b	scalar/vector/matrix	Internal current gain of transistor (hf)
rce	scalar/vector/matrix	Collector to emitter impedance of transistor (1/ho)
rl	scalar/vector/matrix	Load resistor

If arguments are specified as vector/matrix, sizes must match for piecewise mathematical operations.

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rbe/b/rce/rl	Voltage gain ratio

---

power_dB_to_ratio

Calculate power ratio for given dB value.

$$\begin{array}{ccc}{v}_p& =& {10}^{v_{p,\text{dB}}/10\text{dB}}\end{array}$$

 

[gainratio] = power_dB_to_ratio(gaindb);

Argument list

Name	Type	Purpose
gaindb	scalar/vector/matrix	Power gain specified in dB

Result list

Name	Type	Purpose
gainratio	scalar/vector/matrix Same size as gaindb	Power gain ratio

---

power_ratio_to_dB

Calculate dB value for power gain ratio.

$$\begin{array}{ccc}{v}_{p,\text{dB}}& =& 10\text{dB}·{\log }_{10}{v}_p\end{array}$$

 

[gaindb] = power_ratio_to_dB(gainratio);

Argument list

Name	Type	Purpose
gainratio	scalar/vector/matrix	Power gain ratio

Result list

Name	Type	Purpose
gaindb	scalar/vector/matrix Same size as gainratio	dB value for power gain

---

ratio_to_dB

Calculate dB value for voltage or current gain ratio.

$$\begin{array}{ccc}{v}_{u,\text{dB}}& =& 20\text{dB}·{\log }_{10}{v}_u\\ v_{i,\text{dB}}& =& 20\text{dB}·{\log }_{10}{v}_i\end{array}$$

 

[gaindb] = ratio_to_dB(gainratio);

Argument list

Name	Type	Purpose
gainratio	scalar/vector/matrix	Voltage or current gain ratio

Result list

Name	Type	Purpose
gaindb	scalar/vector/matrix Same size as gainratio	dB value for voltage or current gain

---

round_leading_digits

Round numeric value(s), keep specified number of leading significant digits.

[varargout] = round_leading_digits(ndigs, varargin);

Argument list

Name	Type	Purpose
ndigs	scalar/vector/matrix	Number of leading significant digits to keep
varargin	cell list	List of scalar, vector, or matrix objects containing the values to round.

Result list

Name	Type	Purpose
varargout	cell list Same sizes as varargin	List of scalar, vector, or matrix objects containing the rounded values.

---

y_params_current_gain

Calculate current gain for two-gate circuit and load resistor.

[vi] = y_params_current_gain(y, rl);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vi	scalar/vector/matrix same size as rl	Current gain ratio

---

y_params_input_impedance

Calculate input impedance for two-gate circuit and load resistor.

[ri] = y_params_input_impedance(y, rl);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
ri	scalar/vector/matrix same size as rl	Input impedance

---

y_params_op_characteristics

Calculate operational characteristics for two-gate circuit, generator impedance, and load resistor.

$$\begin{array}{ccc}\left(\begin{array}{c}{\underset{¯}{i}}_1\\ {\underset{¯}{i}}_2\end{array}\right)& =& \left(\begin{array}{cc}{\underset{¯}{y}}_{11}& {\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{22}\end{array}\right)\left(\begin{array}{c}{\underset{¯}{u}}_1\\ {\underset{¯}{u}}_2\end{array}\right)\\ & & \\ {\underset{¯}{v}}_u& =& -\frac{{\underset{¯}{y}}_{21}{\underset{¯}{Z}}_{\text{L}}}{{\underset{¯}{y}}_{22}{\underset{¯}{Z}}_{\text{L}}+1}\\ {\underset{¯}{z}}_{\text{i}}& =& \frac{{\underset{¯}{y}}_{22}{\underset{¯}{Z}}_{\text{L}}+1}{{\underset{¯}{y}}_{11}+{\underset{¯}{Z}}_{\text{L}}\det \underset{¯}{y}}\\ {\underset{¯}{z}}_{\text{o}}& =& \frac{{\underset{¯}{y}}_{11}{\underset{¯}{Z}}_{\text{G}}+1}{{\underset{¯}{y}}_{22}+{\underset{¯}{Z}}_{\text{G}}\det \underset{¯}{y}}\\ {\underset{¯}{v}}_i& =& \frac{{\underset{¯}{y}}_{21}}{{\underset{¯}{y}}_{11}+{\underset{¯}{Z}}_{\text{L}}\det \underset{¯}{y}}\end{array}$$

 

[vu, ri, ro, vi] = y_params_op_characteristics(y, rg, rl);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix
rg	scalar/vector/matrix	Generator impedance
rl	scalar/vector/matrix	Load resistor

If both rg and rl are specified as vector or matrix, they must have the same size.

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rg / rl	Voltage gain ratio
ri	scalar/vector/matrix same size as rg / rl	Input impedance
ro	scalar/vector/matrix same size as rg / rl	Output impedance
vi	scalar/vector/matrix same size as rg / rl	Current gain ratio

---

y_params_output_impedance

Calculate output impedance for two-gate circuit and generator impedance.

[ro] = y_params_output_impedance(y, rg);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix
rg	scalar/vector/matrix	Generator impedance

Result list

Name	Type	Purpose
ro	scalar/vector/matrix same size as rg	Output impedance

---

y_params_resistor_horizontal

Create Y parameter set matrix for horizontal resistor.

$$\left(\begin{array}{cc}{\underset{¯}{y}}_{11}& {\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{22}\end{array}\right)=\left(\begin{array}{cc}\frac{1}{\underset{¯}{Z}}& -\frac{1}{\underset{¯}{Z}}\\ -\frac{1}{\underset{¯}{Z}}& \frac{1}{\underset{¯}{Z}}\end{array}\right)$$

 

[y] = y_params_resistor_horizontal(r);

Argument list

Name	Type	Purpose
r	scalar	Horizontal resistor

Result list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

---

y_params_to_a

Convert Y parameter set matrix to A parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{a}}_{11}& {\underset{¯}{a}}_{12}\\ {\underset{¯}{a}}_{21}& {\underset{¯}{a}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{y}}_{21}}·\left(\begin{array}{cc}-{\underset{¯}{y}}_{22}& -1\\ -\det \underset{¯}{y}& -{\underset{¯}{y}}_{11}\end{array}\right)$$

 

[a] = y_params_to_a(y);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

Result list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

---

y_params_to_h

Convert Y parameter set matrix to H parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11}& {\underset{¯}{h}}_{12}\\ {\underset{¯}{h}}_{21}& {\underset{¯}{h}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{y}}_{11}}·\left(\begin{array}{cc}1& -{\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& \det \underset{¯}{y}\end{array}\right)$$

 

[h] = y_params_to_h(y);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

Result list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

---

y_params_to_k

Convert Y parameter set matrix to K parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{k}}_{11}& {\underset{¯}{k}}_{12}\\ {\underset{¯}{k}}_{21}& {\underset{¯}{k}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{y}}_{22}}·\left(\begin{array}{cc}\det \underset{¯}{y}& {\underset{¯}{y}}_{12}\\ -{\underset{¯}{y}}_{21}& 1\end{array}\right)$$

 

[k] = y_params_to_k(y);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

Result list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

---

y_params_to_z

Convert Y parameter set matrix to Z parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{z}}_{11}& {\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{22}\end{array}\right)=\frac{1}{\det \underset{¯}{y}}·\left(\begin{array}{cc}{\underset{¯}{y}}_{22}& -{\underset{¯}{y}}_{12}\\ -{\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{11}\end{array}\right)$$

 

[z] = y_params_to_z(y);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

Result list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

---

y_params_voltage_gain

Calculate voltage gain for two-gate circuit and load resistor.

[vu] = y_params_voltage_gain(y, rl);

Argument list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rl	Voltage gain ratio

---

z_params_current_gain

Calculate current gain for two-gate circuit and load resistor.

[vi] = z_params_current_gain(z, rl);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vi	scalar/vector/matrix same size as rl	Current gain ratio

---

z_params_input_impedance

Calculate input impedance for two-gate circuit and load resistor.

[ri] = z_params_input_impedance(z, rl);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
ri	scalar/vector/matrix same size as rl	Input impedance

---

z_params_op_characteristics

Calculate operational characteristics for two-gate circuit, generator impedance, and load resistor.

$$\begin{array}{ccc}\left(\begin{array}{c}{\underset{¯}{u}}_1\\ {\underset{¯}{u}}_2\end{array}\right)& =& \left(\begin{array}{cc}{\underset{¯}{z}}_{11}& {\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{22}\end{array}\right)\left(\begin{array}{c}{\underset{¯}{i}}_1\\ {\underset{¯}{i}}_2\end{array}\right)\\ & & \\ {\underset{¯}{v}}_u& =& \frac{{\underset{¯}{z}}_{21}{\underset{¯}{Z}}_{\text{L}}}{{\underset{¯}{z}}_{11}{\underset{¯}{Z}}_{\text{L}}+\det \underset{¯}{z}}\\ {\underset{¯}{z}}_{\text{i}}& =& \frac{{\underset{¯}{z}}_{11}{\underset{¯}{Z}}_{\text{L}}+\det \underset{¯}{z}}{{\underset{¯}{z}}_{22}+{\underset{¯}{Z}}_{\text{L}}}\\ {\underset{¯}{z}}_{\text{o}}& =& \frac{{\underset{¯}{z}}_{22}{\underset{¯}{Z}}_{\text{G}}+\det \underset{¯}{z}}{{\underset{¯}{z}}_{11}+{\underset{¯}{Z}}_{\text{G}}}\\ {\underset{¯}{v}}_i& =& -\frac{{\underset{¯}{z}}_{21}}{{\underset{¯}{z}}_{22}+{\underset{¯}{Z}}_{\text{L}}}\end{array}$$

 

[vu, ri, ro, vi] = z_params_op_characteristics(z, rg, rl);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix
rg	scalar/vector/matrix	Generator impedance
rl	scalar/vector/matrix	Load resistor

If both rg and rl are specified as vector or matrix, they must have the same size.

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rg / rl	Voltage gain ratio
ri	scalar/vector/matrix same size as rg / rl	Input impedance
ro	scalar/vector/matrix same size as rg / rl	Output impedance
vi	scalar/vector/matrix same size as rg / rl	Current gain ratio

---

z_params_output_impedance

Calculate output impedance for two-gate circuit and generator impedance.

[ro] = z_params_output_impedance(z, rg);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix
rg	scalar/vector/matrix	Generator impedance

Result list

Name	Type	Purpose
ro	scalar/vector/matrix same size as rg	Output impedance

---

z_params_resistor_vertical

Create Z parameter set matrix for vertical resistor.

$$\left(\begin{array}{cc}{\underset{¯}{z}}_{11}& {\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{22}\end{array}\right)=\left(\begin{array}{cc}\underset{¯}{Z}& \underset{¯}{Z}\\ \underset{¯}{Z}& \underset{¯}{Z}\end{array}\right)$$

 

[z] = z_params_resistor_vertical(r);

Argument list

Name	Type	Purpose
r	scalar	Vertical resistor value.

Result list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix.

---

z_params_to_a

Convert Z parameter set matrix to A parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{a}}_{11}& {\underset{¯}{a}}_{12}\\ {\underset{¯}{a}}_{21}& {\underset{¯}{a}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{z}}_{21}}·\left(\begin{array}{cc}{\underset{¯}{z}}_{11}& \det \underset{¯}{z}\\ 1& {\underset{¯}{z}}_{22}\end{array}\right)$$

 

[a] = z_params_to_a(z);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

Result list

Name	Type	Purpose
a	2×2 matrix	A parameter set matrix

---

z_params_to_h

Convert Z parameter set matrix to H parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{h}}_{11}& {\underset{¯}{h}}_{12}\\ {\underset{¯}{h}}_{21}& {\underset{¯}{h}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{z}}_{22}}·\left(\begin{array}{cc}\det \underset{¯}{z}& {\underset{¯}{z}}_{12}\\ -{\underset{¯}{z}}_{21}& 1\end{array}\right)$$

 

[h] = z_params_to_h(z);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

Result list

Name	Type	Purpose
h	2×2 matrix	H parameter set matrix

---

z_params_to_k

Convert Z parameter set matrix to K parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{k}}_{11}& {\underset{¯}{k}}_{12}\\ {\underset{¯}{k}}_{21}& {\underset{¯}{k}}_{22}\end{array}\right)=\frac{1}{{\underset{¯}{z}}_{11}}·\left(\begin{array}{cc}1& -{\underset{¯}{z}}_{12}\\ {\underset{¯}{z}}_{21}& \det \underset{¯}{z}\end{array}\right)$$

 

[k] = z_params_to_k(z);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

Result list

Name	Type	Purpose
k	2×2 matrix	K parameter set matrix

---

z_params_to_y

Convert Z parameter set matrix to Y parameter set matrix.

$$\left(\begin{array}{cc}{\underset{¯}{y}}_{11}& {\underset{¯}{y}}_{12}\\ {\underset{¯}{y}}_{21}& {\underset{¯}{y}}_{22}\end{array}\right)=\frac{1}{\det \underset{¯}{z}}·\left(\begin{array}{cc}{\underset{¯}{z}}_{22}& -{\underset{¯}{z}}_{12}\\ -{\underset{¯}{z}}_{21}& {\underset{¯}{z}}_{11}\end{array}\right)$$

 

[y] = z_params_to_y(z);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix

Result list

Name	Type	Purpose
y	2×2 matrix	Y parameter set matrix

---

z_params_voltage_gain

Calculate voltage gain for two-gate circuit and load resistor.

[vu] = z_params_voltage_gain(z, rl);

Argument list

Name	Type	Purpose
z	2×2 matrix	Z parameter set matrix
rl	scalar/vector/matrix	Load resistor

Result list

Name	Type	Purpose
vu	scalar/vector/matrix same size as rl	Voltage gain ratio

---

Literature and information sources

[BB90]		K. Bystron und J. Borgmeyer Grundlagen der Technischen Elektronik 2. Auflage Carl Hanser Verlag München Wien ISBN: 3-446-15869-3 Calculations with physical parameters Coupling capacitors, emitter capacitors Formulas to convert between H parameter sets for common emitter, common base, and common collector circuit
[HEG19]		Hering, Endres, Gutekunst Elektronik für Ingenieure und Naturwissenschaftler 8. Auflage Springer Vieweg ISBN: 978-3662626979 Formulas to calculate operational conditions with H, Z, Y, and A parameters Formulas to convert between H, Z, Y, and A parameters
[Wikipedia]		https://de.wikipedia.org/wiki/Zweitor Formulas to convert between H, Z, Y, and A parameters
[ElectronicsPlanet]		https://www.electronicsplanet.ch/Widerstand/Widerstandsreihe-E192.htm E series values
[wxMaxima]		http://wxmaxima-developers.github.io/wxmaxima/ Among others the program can solve systems of equations. This was used to find / check formulas for operational conditions.