**Introduction:**

When we discuss resistance (or resistors) we need to also consider Conductive properties as well, measured in Mhos.

I dare say that most of us avoid thinking this way, but perhaps sometimes it can be quite relevant.

In many areas of electronics we need to deal with "reciprical values":

Frequency vs Time, and Resistance vs Conductance, to name a couple.

And while we are at it, we
need to remember that **"..illities"**
and **"..ivities"**
are "**properties"**.

In tubes and FETs we often measure something called "* Conductivity vs Conductance

* Resistivity vs Resistance

* Reluctivity vs Reluctance

* Permeabilty vs Permeance

When FETs first came out, they were nicknamed "Space-Transistors" or simply "Spacistors" because they behaved more like vacumn tubes, as voltage controlled devices, rather than current controlled devices.

In
**Illustration
#1**
we have a conventional Series Circuit, where we have resistances that
simply add, and with common current and directlly proportional
voltage (IR) drops.

Now consider that where Conductance is the reciprical of Resistance, we have a whole new approach to the same circuit in Illustration #1a.

Perhaps
now we understand why in **Illustration
#2**
we use that peculiar formula of recipricals, because in parallel
considerations we can add conductances and then convert back to
resistance.

Many also tend to forget that conductance is mewasured in "Mhos"

This
Series-Parallel-Combination-Circuit in **Illustration
#3**
has been my favorite for many years,, where folks have to deal with
combining serial values with parallel values to determine the total
resistance. Then dealing with voltage divisions and current division
combinations. Finally, there are numerous "deductive problems"
using single IR drops or single current allocations, or polarity
potential assignments, with no ground references.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

**Now
the imfamous "Ladder Circuit":**

**Illustration
#4** shows how the Series-Parallel computations are
performed down to the Total, and then common voltage and common
currents are used to perform expansions back out to RL.

**Illustration
#5** shows more detail of the computations involved used in
Illustration #4. Please note the simple schematic at the top of the
page. Wouldn't it be great if that could represent the complexity of
all the values in the ladder circuit, as an "equivelant" to
simplify changes in the load? The answer is 'yes', and it's call the
**"Thevinin Equivelant
Circuit Analysis"**
method.

Moving on to **Illustration
#5a**, is how this is acomplished:

**First**,
remove the load RL to create an open circuit. Note that with no
current flowing through R3 or R8, there are no voltage drops, and so
we drop them out of our calculations as we compute everything toward
the source, and then back out to the open circuit, which we determine
to be **1.407V** accross
the open circuit.

This is called **"EOC"**,
as in **"Voltage of the
Open Circuit Variety".**

**Secondly,**
in **Illustration
#5b**,
replace the source with it's internal resistance, and compute what an
Ohmmeter would measure as a substitute for RL. This should calculate
to be **15.343K
Ohms, **called
**"R-Thev".
**This
value represents the "Equivalent Resistive Value" for the
entire Ladder Circuit, minus the Load.

**Thirdly,**
we can now compose the "EOC" as a new source voltage, and
have the **"R-Thev"**
as a simple Series Circuit to drive the Load RL.

**Illustration
#5c** shows that by
presenting the load RL (of any value) we can easily calculate the
resulting current and IR drop accross RL. We also can now easily see
that there is a set of "Min-Max" value limitations of both
currents and voltages, similar to what we use as "Projected Load
Lines" for either vacumn tube or transistor circuit designs.

**Illustration
#5d** allows us to see a
couple of remarkable equivalent circuit considerations:

**First**,
it turns out that in **Illustration
#5c**, we calulate that a
short circuit current would be **91.7microamps**,
which we call **"ISC".**

**Secondly****,
**there
is a method of using that ISC as a **"Current-Source"**,
rather than a Voltage Source, and then placing the * equivalent
resistive value*
in

This
version is called a **"Norton's
Equivalent Circuit Analysis"**,
and especially note that the two are * directly
interchangeable*
one to the other.

Finally, for those who are
interested, you can download and execute the **"Ladder_Circuit.exe"**
here, which has all these initial "given" values and
compute all currents, voltages and even power values. EOC and ISC
are also availble, with appropriate circuit illustrations.**"EOC"**
and **"ISC"**
computations are also available. Allows changing any value and instant re-computations.

**WA7RSO – 12/25/2020**