Scientific notation in SPICE
The SPICE circuit simulation computer program uses scientific
notation to display its output information, and can interpret both
scientific notation and metric prefixes in the circuit description
files. If you are going to be able to successfully interpret the
SPICE analyses throughout this book, you must be able to understand
the notation used to express variables of voltage, current, etc. in
the program.
Let's start with a very simple circuit composed of one voltage
source (a battery) and one resistor:
To simulate this circuit using SPICE, we first have to designate
node numbers for all the distinct points in the circuit, then list
the components along with their respective node numbers so the
computer knows which component is connected to which, and how. For a
circuit of this simplicity, the use of SPICE seems like overkill,
but it serves the purpose of demonstrating practical use of
scientific notation:
Typing out a circuit description file, or netlist, for
this circuit, we get this:
simple circuit
v1 1 0 dc 24
r1 1 0 5
.end
The line "v1 1 0 dc 24" describes the battery,
positioned between nodes 1 and 0, with a DC voltage of 24 volts. The
line "r1 1 0 5" describes the 5 Ω resistor placed between
nodes 1 and 0.
Using a computer to run a SPICE analysis on this circuit
description file, we get the following results:
node voltage
( 1) 24.0000
voltage source currents
name current
v1 -4.800E+00
total power dissipation 1.15E+02 watts
SPICE tells us that the voltage "at" node number 1 (actually,
this means the voltage between nodes 1 and 0, node 0 being the
default reference point for all voltage measurements) is equal to 24
volts. The current through battery "v1" is displayed as -4.800E+00
amps. This is SPICE's method of denoting scientific notation. What
it's really saying is "-4.800 x 100 amps," or simply
-4.800 amps. The negative value for current here is due to a quirk
in SPICE and does not indicate anything significant about the
circuit itself. The "total power dissipation" is given to us as
1.15E+02 watts, which means "1.15 x 102 watts," or 115
watts.
Let's modify our example circuit so that it has a 5 kΩ (5
kilo-ohm, or 5,000 ohm) resistor instead of a 5 Ω resistor and see
what happens.
Once again is our circuit description file, or "netlist:"
simple circuit
v1 1 0 dc 24
r1 1 0 5k
.end
The letter "k" following the number 5 on the resistor's line
tells SPICE that it is a figure of 5 kΩ, not 5 Ω. Let's see what
result we get when we run this through the computer:
node voltage
( 1) 24.0000
voltage source currents
name current
v1 -4.800E-03
total power dissipation 1.15E-01 watts
The battery voltage, of course, hasn't changed since the first
simulation: it's still at 24 volts. The circuit current, on the
other hand, is much less this time because we've made the resistor a
larger value, making it more difficult for electrons to flow. SPICE
tells us that the current this time is equal to -4.800E-03 amps, or
-4.800 x 10-3 amps. This is equivalent to taking the
number -4.8 and skipping the decimal point three places to the left.
Of course, if we recognize that 10-3 is the same as
the metric prefix "milli," we could write the figure as -4.8
milliamps, or -4.8 mA.
Looking at the "total power dissipation" given to us by SPICE on
this second simulation, we see that it is 1.15E-01 watts, or 1.15 x
10-1 watts. The power of -1 corresponds to the metric
prefix "deci," but generally we limit our use of metric prefixes in
electronics to those associated with powers of ten that are
multiples of three (ten to the power of . . . -12, -9, -6, -3, 3, 6,
9, 12, etc.). So, if we want to follow this convention, we must
express this power dissipation figure as 0.115 watts or 115
milliwatts (115 mW) rather than 1.15 deciwatts (1.15 dW).
Perhaps the easiest way to convert a figure from scientific
notation to common metric prefixes is with a scientific calculator
set to the "engineering" or "metric" display mode. Just set the
calculator for that display mode, type any scientific notation
figure into it using the proper keystrokes (see your owner's
manual), press the "equals" or "enter" key, and it should display
the same figure in engineering/metric notation.
Again, I'll be using SPICE as a method of demonstrating circuit
concepts throughout this book. Consequently, it is in your best
interest to understand scientific notation so you can easily
comprehend its output data format.
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