Changes

There are four input parameters:

There are four input parameters:

* Input current: <math>I_{in}</math> (A)

* Input current: I_in (A)

* Bias voltage: <math>V_b</math> (V)

* Bias voltage: V_b (V)

* Power voltage: <math>V_c</math> (V)

* Power voltage: V_c (V)

* Frequency: <math>f</math> (Hz)

* Frequency: f (Hz)

=== Unknown variables ===

=== Unknown variables ===

There are twenty-four unknown variables.  The locations (and directions in the case of currents) are labeled on the circuit diagram.  All unknowns are assumed to be of the form

There are twenty-four unknown variables.  The locations (and directions in the case of currents) are labeled on the circuit diagram.  All unknowns are assumed to be of the form

: <math>X(t) = X_0 e^{i \omega t} + X_1\,\!</math>,<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->

: <math>X(t) = X_0 e^{i \omega t} + X_1\,\!</math>,

where <math>X_0</math> gives the amplitude of oscillation, or the AC component, and <math>X_1</math> gives the DC offset.

where X₀ gives the amplitude of oscillation, or the AC component, and X₁ gives the DC offset.

* Node voltages: <math>V_1</math>, <math>V_2</math>, <math>V_3</math>, <math>V_4</math>, <math>V_5</math>, <math>V_7</math>, <math>V_{out}</math>

* Node voltages: V₁, V₂, V₃, V₄, V₅, V₇, V_out

** Note: there is no <math>V_6</math> on this circuit; it was a redundant variable with <math>V_c</math>.

** Note: there is no V₆ on this circuit; it was a redundant variable with V_c.

* Resistor currents: <math>I_1</math>, <math>I_2</math>, <math>I_3</math>, <math>I_4</math>, <math>I_5</math>, <math>I_6</math>, <math>I_7</math>, <math>I_t</math>

* Resistor currents: I₁, I₂, I₃, I₄, I₅, I₆, I₇, I_t

* Transistor currents: <math>j_b</math>, <math>j_c</math>, <math>j_e</math>, <math>k_b</math>, <math>k_c</math>, <math>k_e</math>

* Transistor currents: j_b, j_c, j_e, k_b, k_c, k_e

* Capacitor currents: <math>h_1</math>, <math>h_2</math>, <math>h_3</math>

* Capacitor currents: h₁, h₂, h₃

=== Constants ===

=== Constants ===

| ''Component'' || ''Resistance''

| ''Component'' || ''Resistance''

|-

|-

| <math>R_1</math> || <math>100\mbox{k}\Omega</math>

| R₁ || 100k&#937;

|-

|-

| <math>R_2</math> || <math>10\mbox{k}\Omega</math>

| R₂ || 10k&#937;

|-

|-

| <math>R_3</math> || <math>5.6\mbox{k}\Omega</math>

| R₃ || 5.6k&#937;

|-

|-

| <math>R_4</math> || <math>1.39\mbox{k}\Omega</math>

| R₄ || 1.39k&#937;

|-

|-

| <math>R_5</math> || <math>1\mbox{k}\Omega</math>

| R₅ || 1k&#937;

|-

|-

| <math>R_6</math> || <math>53\Omega</math>

| R₆ || 53&#937;

|-

|-

| <math>R_7</math> || <math>1.55\mbox{k}\Omega</math>

| R₇ || 1.55k&#937;

|-

|-

| <math>R_t</math> || <math>50\Omega</math>

| R_t || 50&#937;

|}

|}

==== Capacitors ====

==== Capacitors ====

The capacitors are not labeled on the amplifier itself or in the documentation supplied with the amplifier, so the following values are guesses as to the capacitances.  Note that <math>C_4</math> does not exist.

The capacitors are not labeled on the amplifier itself or in the documentation supplied with the amplifier, so the following values are guesses as to the capacitances.  Note that C₄ does not exist.

{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:left"

{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:left"

| ''Component'' || ''Capacitance''

| ''Component'' || ''Capacitance''

|-

|-

| <math>C_1</math> || <math>100\mbox{nF}</math>

| C₁ || 100nF

|-

|-

| <math>C_2</math> || <math>0.1\mbox{nF}</math>

| C₂ || 0.1nF

|-

|-

| <math>C_3</math> || <math>100\mbox{nF}</math>

| C₃ || 100nF

|-

|-

| <math>C_5</math> || <math>10\mbox{nF}</math>

| C₅ || 10nF

|}

|}

{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:left"

{| align="center" border="0" cellpadding="8" cellspacing="0" style="text-align:left"

| ''Parameter'' || ''Description'' || <math>T_1</math> ''value'' || <math>T_2</math> ''value''

| ''Parameter'' || ''Description'' || T₁ ''value'' || T₂ ''value''

|-

|-

| VT || temperature voltage || 0.0259 || 0.0259

| VT || temperature voltage || 0.0259 || 0.0259

|-

|-

| BF || ideal forward maximum <math>\beta</math> || 93 || 34

| BF || ideal forward maximum &#946; || 93 || 34

|-

|-

| NF || forward current emission coefficient || 0.99 || 1.0

| NF || forward current emission coefficient || 0.99 || 1.0

| NE || B-E leakage emission coefficient || 1.46 || 1.94

| NE || B-E leakage emission coefficient || 1.46 || 1.94

|-

|-

| RB || zero-bias base resistance || 21<math>\Omega</math> || 5<math>\Omega</math>

| RB || zero-bias base resistance || 21&#937; || 5&#937;

|-

|-

| RE || emitter resistance || 0.37<math>\Omega</math> || 1<math>\Omega</math>

| RE || emitter resistance || 0.37&#937; || 1&#937;

|}

|}

=== Transistor operating point ===

=== Transistor operating point ===

Each transistor has an operating point, <math>U_1</math> and <math>U_2</math>.  Both are initially assumed to be 0.7V.  Under DC conditions (<math>I_{in} = 0</math>A, <math>f = 0</math>Hz) we iterate on U to refine these two parameters.  Each iteration refines the operating point by averaging the current operating point with the associated <math>V_{be}</math>.  <math>V_{be}</math> is the base-to-emitter voltage of the transistor and is given by

Each transistor has an operating point, U₁ and U₂.  Both are initially assumed to be 0.7V.  Under DC conditions (I_in = 0A, f = 0Hz) we iterate on U to refine these two parameters.  Each iteration refines the operating point by averaging the current operating point with the associated V_be.  V_be is the base-to-emitter voltage of the transistor and is given by

* <math>V_{be1} = V_3</math>

* V_be1 = V₃

* <math>V_{be2} = V_7 - V_4</math>.

* V_be2 = V₇ - V₄.

=== Derived parameters ===

=== Derived parameters ===