Introduction to
Electronic Circuits
Error Calculations
Component Tolerance & Power Rating
Real Voltage & Current Sources
Real Measurements
Error Calculations (Review)
Error is generally equal to the absolute value of:
Expected value (voltage, current, etc.) – Measured value (voltage, current, etc.)
In circuit analysis, however, the expected value can be calculated many
different ways. For example:
1.  Does one use the ideal value of a battery or the measured value?
2.  Does one use the nominal value of a resistor or the measured value?
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In most cases, expected value is the theoretical value of a circuit parameter using an
ideal model of the circuit and ideal or nominal values for the circuit components. In
the following example, R1, R2 = 10 kOhms; R3 = 1.5 kOhms; and R4 = 4.7 kOhms. To
calculate the expected value of the voltage across R4, we would use 9V for the voltage
source; 10,000 for R1 and R2; 1,500 for R3 and 4,700 for R4)
9V
-
R2
R1
R4
R3
Percentage Error Calculations(Review)
Percentage Error is generally equal to:
100% * Error/Expected Value
In the following circuit, the expected value of the voltage of R4 is calculated using 9V
for the voltage source; 10,000 for R1 and R2; 1,500 for R3 and 4,700 for R4. The
measured value of that same voltage is that read by a voltmeter or similar instrument
across R4.
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It is always important to ensure that the measurement instrument has minimal effect
on the measurement itself. For example, if the value of the resistor R4 in the circuit
below were very large (on the order of MegaOhms), it is likely that a portable
multimeter (and its large, but not infinite internal resistance) would interfere with the
measurement of the voltage across R4 and introduce its own error.
9V
-
R2
R1
R4
R3
Component Tolerance (Review)
Real components (capacitors, inductors, resistors) have a nominal value and
a tolerance. For example:
1.  A 10,000 ohm resistor with 5% tolerance has a nominal value of 10,000
ohms but actual resistor values can vary between 9,500 and 10,500 ohms.
2.  A 1 µF capacitor with a 10% tolerance has a nominal value of 1µF but
actual capacitor values can vary between 0.90 µF and 1.10 µF
The 5% tolerance of the two resistors in the circuit below means that the
voltage Va can vary between 4.275 and 4.725 V depending on the actual
values of the resistors.
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Va
9V
-
R1
R4
R1
R4
Va
9500
9500
4.5V
9500
10500
4.275
10500
9500
4.725
10500
10500
4.5
R1 and R4 are both 5% tolerance resistors with a nominal value of 10,000 ohms
Power Rating
Real resistors have power ratings which define how much power they can
consistently dissipate without degrading performance
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1.  A ¼ Watt resistor can only dissipate a maximum of ¼ Watt of heat/power
effectively over long term operation.
2.  Exceeding the power rating of a resistor at best will push the resistor out
of tolerance (as it heats, the resistance of the resistor will change). At
worst, the resistor will burn out and produce smoke, failing entirely.
Vdd
-
R1
R4
The resistors R1 and R4 in
the circuit to the left have a
nominal value of 100 ohms,
have a 5% tolerance, and are
rated to a 1/4 Watt. How
high can the power supply
Vdd be before the resistors
degrade?
The voltage across each resistor is approximately Vdd/2. Thus, the power
dissipated by each resistor is (Vdd2/4)/100. Thus, a value of Vdd higher than
10V will result in more than ¼ W being dissipated in the resistors.
Real Voltage Sources
A real voltage source has an internal resistance to current flow. This internal
resistance Rs can be “modeled” by placing a resistor Rs in series with the
voltage associated with the source.
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For example, a 9V battery can be “modeled” as a 9V independent voltage
source in series with its internal resistance Rs.
9V
-
Rs
Rload
In a high quality battery,
the value of Rs is
designed to be small.
Knowing this, how can we
manipulate Rload (an
external resistor that we
choose) to determine Rs?
Real Current Sources
A real current source also has an internal resistance to current flow. This
internal resistance Rs can be “modeled” by placing a resistor Rs in parallel
with the current associated with the source.
However, unlike voltage sources which have a physical equivalent in a battery,
current sources do not often have a direct physical equivalent.
I
Rs
A current source in
parallel with an internal
resistance is equivalent
(in the power it is able to
deliver to a circuit) to a
voltage source in series
with that same internal
resistance!
Real Circuits
A real circuit can be modeled by a single voltage source in series with a single
resistance. This model is called a Thevenin equivalent circuit.
In a previous slide, we manipulated Rload to figure out the internal resistance of
a battery -- Rs.
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We can do the same thing with any circuit to find the Thevenin voltage (V? in
the circuit below, often labeled Vthevenin) and the Thevenin resistance R? in the
circuit below (often labeled Rthevenin).
V?
-
R?
Rload
How can we manipulate
the value of Rload in the
circuit to the left to find
R? (Rthevenin) and V?
(Vthevenin)?
Real Measurements
When measuring voltage, a real multimeter can be modeled as a resistance
in parallel with the voltage being measured.
This resistance is typically very large (for example, 25 MegaOhms in a
portable Fluke Multimeter).
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Only when measuring voltages across large resistance does this internal
resistance become a source of error.
9V
-
1MOhm
Rload
How much error does the
Fluke Multimeter
introduce in measuring
the voltage across Rload if
Rload is 25 MegaOhms?
Real Measurements
When measuring resistance, a real multimeter injects a small amount of
current into the resistor and measures the resulting voltage. Then Ohm’s Law
is used to compute the measured resistance.
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The right amount of current needs to be injected to develop a measurable
voltage across the resistor (not too small, not too large). Thus, many
multimeters have a scale, where the user must select the right range of
resistors in order to get an accurate resistance value.
9V
-
1MOhm
Rload
Where does error arise in
the Multimeter during
the measurement of
resistance?
Real Measurements
Real World
Things rarely operate as we expect or design them to…
The challenge then becomes designing in such a way that the difference
between the ideal and the real does not become the difference between
functional and useless.