ELECTRONIC DESIGN NOTES #3  RESISTORS

In Electronic Design Notes #1
was mentioned we can control the current passing through electrical circuits using resistors. Of course, there are other means
to achieve good current control, but resistors are simple, cheap, and very efficient electronic components.
Control is the true magic word in electronics. No matter what we do, the purpose is to take control
over voltages,
currents, frequencies, and over various functions. Once we achieve total control, then we can do whatever we can
think of. Resistors help us control all electrical characteristics that
are calculated based on resistance: that is, current, voltage, frequency, etc.
There are a few basic things we need to know about resistors, therefore they are listed summarily as follows:
1. Types of Resistors
2. Useful Formulas
3. Resistors Color Code Chart
4. Equivalent Series and Parallel Resistors
5. Controlling Voltages and Currents
6. Detecting Current Sense
7. Frequency Control
NOTE The basic
notions highlighted in this page are related to a few electronic
design topics presented in the first part, Hardware Design, of
LEARN HARDWARE FIRMWARE AND SOFTWARE
DESIGN.

1. TYPES OF RESISTORS
There is an incredible variety of resistors, though in this page are presented only
a few main groups. First of all,
resistors are groped in:
A. fixed
B. variable
Depending on the way we insert them into electrical circuits, resistors can be:
a. through hole (TH)
b. surface mount (SM)
c. various mechanical fixtures
Further, resistors are built as:
1. carbon composition
2. metal film
3. carbon film
4. wirewound
Of course we could differentiate resistors based on the power (current) they can safely handle, but there are way
too many types available.
Variable resistors come in a few particular types. They are important to note
here because each type requires
specific schematics:
1. potentiometers 2. rheostats 3. decades 4. programmable potentiometers (details of hardware schematics and firmware programming source code are
presented in LEARN HARDWARE
FIRMWARE AND SOFTWARE DESIGN)


Fig1: Rheostat and Potentiometer
wiring Schematics
The Rheostat circuit is used to control currents (Iv)
The Potentiometer circuit is used to control voltages (Uv) 

2. USEFUL FORMULAS
In order to work with resistors we need a few formulas, as follows:

RESISTORS' FORMULAS 
FORMULA 
NAME 
R [Ω]= ρ * L / A 
Resistance (details are in
Design Notes 1) 
R [Ω] = U [V] / I [A] 
Ohm's Law in DC circuits
(details are in Design Notes 1) 
Z [Ω] = U [V] / I [A] 
Ohm's Law in AC circuits (details are in Design Notes 1) 
Z = √[R^{2} + (X_{L}  X_{c})^{2}] 
Impedance (details are in
Design Notes 1) 
X_{L }[Ω] = 2*PI*f [Hz]*L [H] 
Inductive Reactance 
X_{c }[Ω]= 1/2*PI*f [Hz]*C [C] 
Capacitive Reactance 
R_{t} = R_{o} * (1 + α * t) 
R_{t} =
Resistance at current
temperature
R_{o} = resistance at 0 Celsius
t = actual temperature
α = temperature coefficient of resistivity 
G [Siemens] = 1 / R 
Conductance 
σ = 1/ρ 
Electrical conductivity 
P [W] = U [V] * I [A]
P [W] = I^{2}[A] * R [Ω] 
DC power 
1 [hp] = 746 [W] 
Conversion to horsepower 
1 [kW] = 1.34 [hp] 
Conversion to kilowatt 
W [J] = U [V] * I [A] * T [s] 
DC Energy 
η = Pout / Pin 
Efficiency 

3. RESISTORS COLOR CODE CHART
Fixed resistors of the "through hole" type are marked using a special color code.
The new SM (surface mount) types are marked using numbering systems specific to each manufacturerplease consult
their Data Sheets.

RESISTOR COLOR CODE 

Color 
1st Band 
2nd Band 
3rd Band 
Multiplier 
Tolerance 

Black 
0 
0 
0 
10^{0} 
 

Brown 
1 
1 
1 
10^{1} 
(+/)1% 

Red 
2 
2 
2 
10^{2} 
(+/)2% 

Orange 
3 
3 
3 
10^{3} 
(+/)3% 

Yellow 
4 
4 
4 
10^{4} 
(+/)4% 

Green 
5 
5 
5 
10^{5} 
(+/)0.5% 

Blue 
6 
6 
6 
10^{6} 
(+/)0.25% 

Violet 
7 
7 
7 
10^{7} 
(+/)0.1% 

Gray 
8 
8 
8 
10^{8}/10^{2} 
 

White 
9 
9 
9 
10^{9}/10^{1} 
 

Gold 
 
 
 
10^{1} 
(+/)5% 

Silver 
 
 
 
10^{2} 
(+/)10% 

None 
 
 
 
 
(+/)20% 

NOTE The third
color band could be missing.

4. EQUIVALENT SERIES AND PARALLEL RESISTORS
The equivalent of series resistors is calculated with:
R_{T }=
Σ R_{i}
The equivalent of parallel resistors is calculated with:
1/R_{T} = Σ 1/R_{i}
Calculation examples for three resistors are presented next.


Fig 2: The equivalent resistance of 3 series resistors
R_{T} = R_{1} + R_{2}
+ R_{3}
R_{T} = 2K +3K + 4K = 9K
The series equivalent R_{T} is greater than the greatest component


Fig 3: The equivalent resistance of 3 resistors in parallel
1/R_{T} = 1/R_{1} +1/R_{2}
+ 1/R_{3}
R_{T} = R1*R2*R3 / (R2*R3 + R1*R3 +R1*R2)
R_{T} = 24 / (12 + 8 + 6) = 24 / 26 = 0.923K
The parallel equivalent R_{T} is always smaller than the smallest component


5. CONTROLLING VOLTAGES AND CURRENTS
First thing, please take a look at Figs 4 and 5.


Fig 4: Voltage control circuit
Voltage divider formula: U_{i} = (U * R_{i}) / R_{T}
U = 12V = total voltage applied
R_{i} = 3Ω = incremental resistance
R_{T} = 1Ω + 3Ω = 4Ω = total resistance
U_{i }= (12 * 3) / 4 = 9V = incremental voltage


Fig 5: Current control circuit
I_{max} = U / R_{1} = 12 / 3 = 4mA 

In Fig 4, we control the voltage U_{i} using a "voltage divider" schematic.
We can even adjust U_{i} if we use a potentiometer schematic as we did in in Fig 1. The voltage divider
schematic allows for 2, 3,..n precise voltage levels to be supplied to the
"Load" circuit. In Fig 4 are the formulas
needed to calculate the Ui value.
In Fig 5, R1 plays the role of a "current limiter". The meaning of that schematic is, the maximum
current supplied to Load is 4 mA. Even if Load becomes a shortcircuit, the maximum current will not exceed 4 mA.
Please note: using a variable resistor wired as in Fig 1, the Rheostat, we can adjust the maximum/minimum
current supplied to Load.
In both of the above schematics, Figs 4 and 5, we could use programmable potentiometers. Details about the simplest and the most
efficient ways of working with programmable potentiometers are presented in
LEARN HARDWARE
FIRMWARE AND SOFTWARE DESIGN. 
6. DETECTING CURRENT SENSE
Please take a look at Fig 6.


Fig 6:
Detecting the current sense
Possible cases:
V1 > V2 Load is drawing power
V1 = V2 Load is Open
V1 < V2 Load is generating power
V2 = 0 Load is
shortcircuited 

In normal conditions V1 = 12 V, and V2
= 11.988 V (R1 = 1 KΩ). These values are sent to the AnalogtoDecimal channels 1 and 2
(randomly chosen) of the PIC controller. Next, we transform the analog voltages into their decimal equivalents, then we compare them
mathematically. The result is one of the following instances:
V1 > V2 (Load is drawing power) V1 = V2 (Load is Open) V1 < V2 (Load is generating power) V2 = 0 (Load is shortcircuited)
If an accident happens and Load becomes a generator, the current will change its sense, therefore V2 will become
greater than V1:
V2 > V1
Not only that we are able to detect the sense of the current, but we know precisely how much current Load is drawing in
each moment.
Details about working with Microchip dsPIC controllers and about AD conversion are
presented in
LEARN HARDWARE
FIRMWARE AND SOFTWARE DESIGN.
7. FREQUENCY CONTROL
Details about controlling frequency using resistors are presented in Design Notes
#9  Analog Filters.

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