© Jonathan Bartlett 2020
J. BartlettElectronics for Beginnershttps://doi.org/10.1007/978-1-4842-5979-5_9

9. Basic Resistor Circuit Patterns

Jonathan Bartlett1 
(1)
Tulsa, OK, USA
 

When most people look at a schematic drawing, all they see is a sea of interconnected components with no rhyme or reason combining them. However, most circuits are actually a collection of circuit patterns. A circuit pattern is a common way of arranging components to accomplish an electronic task. Experienced circuit designers can look at a circuit and see the patterns that are being used. Instead of a mass of unrelated components, a circuit designer will look at a schematic and perceive a few basic patterns being implemented in a coherent way.

In this chapter, we are going to learn three basic resistor patterns and learn to work with switches as well.

9.1 Switches and Buttons

Switches and buttons are very simple devices, but nonetheless we probably need to take a moment to explain them. A switch works by connecting or disconnecting a circuit. A switch in the “off” position basically disconnects the wires so that the circuit can’t complete. A switch in the “on” position connects the wires.

There are different types of switches depending on their operation. The ones we are concerned with are called “single pole single throw” (SPST) switches, which means that they control only one circuit (single pole) and the only thing they do is turn it on or off (single throw).

Figure 9-1 shows what the schematic symbols for an SPST switch and an SPST momentary switch (i.e., a button) look like. As the drawing indicates, when the switch is open, the circuit disconnects. When the switch closes, it connects the circuit. While the switch holds its position stable (someone has to manually switch it back and forth), the button only connects the circuit while it is being pushed. While the button is being pushed, the circuit is connected, but as soon as someone stops pushing the button, the circuit opens back up.
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Figure 9-1

Schematic Symbols for an SPST Switch (Left) and an SPST Button (Right)

Figure 9-2 shows what a simple circuit with a switch looks like. It is just like a normal LED circuit, but with a switch controlling whether or not electricity can flow. Note that the switch is just as effective on the other side of the circuit. If the switch was the last part of the circuit, it would be equally as effective. Remember, in order for current to flow, there must be a full circuit from positive back to negative.
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Figure 9-2

A Simple Switch Circuit

Switches can also be used to turn on or off individual parts of a circuit—basically reconfiguring the circuit while it is running. In the circuit given in Figure 9-3, a master switch (S1) turns the whole circuit on or off, and two individual switches (S2 and S3) turn parallel branches of the circuit on and off.
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Figure 9-3

A Circuit with Multiple Switches

To analyze a circuit with switches, you need to analyze the way the circuit behaves with each configuration of switches. In this case, obviously when S1 is open, no current at all flows. However, this circuit will use different amounts of current when S2 is closed, S3 is closed, and both S2 and S3 are both closed. Therefore, to truly know the behavior of the circuit, you need to calculate the current usage in each of these situations.

9.2 Current-Limiting Resistor Pattern

The first resistor pattern we are going to learn is one that we already know—the current-limiting resistor pattern. The idea behind this pattern is that a resistor is added to limit the amount of current that can flow through a device. The size of the resistor needed depends on the size of the voltage source, the action of the device itself, and the maximum amount of current to allow. Then, the resistor size needed can be calculated using Ohm’s law.

Many resistors are added to circuits to limit current flow. At the beginning, we used resistors to make sure we didn’t destroy our LEDs. In Chapter 8, we used a resistor to limit the amount of current flowing through our voltage regulation circuit.

In many different circuits, we will need resistors to limit current for two different reasons—to avoid breaking equipment and to save battery life. Oftentimes, we are actually choosing resistor values to accomplish both of these tasks.

If an LED breaks with 20 mA, then we need a resistor big enough to keep the current that low. However, if the LED light is sufficiently visible with 1 mA, then, to save battery life, we might want a bigger resistor. Battery capacity is often measured in milliamp-hours (mAh), with a typical 9 V battery holding 400 mAh. So, with such a battery, an LED circuit at 10 mA will drain the battery in 40 hours (400 mAh/10 mA = 40 h), but the same LED circuit with a bigger resistor, limiting the current to 1 mA, will take a full 400 hours (400 mAh/1 mA = 400 h) to drain the same battery! That will save you a lot of money in the long run.

9.3 Voltage Divider Pattern

A voltage divider occurs anytime there are two resistors together with a subcircuit coming out from in between them. They usually are connected to a fixed positive voltage on one side of the first resistor and the ground on the other side of the second resistor, but this isn’t strictly necessary. A simple schematic of a voltage divider is shown in Figure 9-4. Notice that there are two resistors between the voltage source and the ground (a 1k on top and a 2k on the bottom) and a subcircuit (indicated by the load resistance) branching off from between them. Under certain circumstances (which will be covered in a moment), we can basically ignore the parallel resistance of the subcircuit and just look at the voltages at each point in the main voltage divider circuit.
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Figure 9-4

A Simple Voltage Divider Circuit

9.3.1 Calculating the Voltages

We can see that the voltage at the top of the voltage divider is 9 V (because it connects to the positive terminal) and at the bottom of the voltage divider it is 0 V (because it connects to the negative terminal). Therefore, the total voltage drop across both resistors must be 9 V. Since the resistors are in series (remember, we are ignoring the load for now), we can find the total resistance in the circuit by just adding their resistances. So 1,000 Ω + 2,000 Ω = 3,000 Ω. Since the current in a series is the same for the whole series, we can now use Ohm’s law to calculate the current flow:
$$ I=frac{V}{R}=frac{9mathrm{V}}{3,000Omega}=0.003mathrm{A}=3 mA $$
So there is 0.003 A (3 mA) in this circuit. That means that each resistor in the series will have this amount of current flowing through them. Therefore, we can calculate the voltage drop across each resistor. Let’s look at the 1k resistor:
$$ V=Iast R=0.003;mathrm{A}ast 1,000Omega =3mathrm{V} $$

So the voltage drop across the first resistor is 3 V. That means that, since the battery started at 9 V, at the end of the resistor the voltage compared to ground is 6 V. We can calculate the voltage drop across the second resistor either by Ohm’s law again or just by noting the fact that since the other end of the resistor is connected to ground, the voltage must go from 6 V to 0 V.

Figure 9-5 shows the voltages at each point (relative to ground). As you can see, the wire from the middle of the voltage divider has a new voltage that can be used by the load. This is what voltage dividers are normally for—they have a simple way of providing a scaled-down voltage to a different part of the circuit.
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Figure 9-5

Voltage Divider with Voltages Labeled

9.3.2 Finding Resistor Ratios

But how do we choose the values of the resistors?

One thing to note is that the second resistor consumed exactly twice as much voltage as the first resistor. Additionally, the second resistor was exactly twice as large as the first resistor. Thus, as a general principle, the relative sizes of the resistors will determine the relative amounts of voltage they eat up. So, if we needed a 4.5 V output—that is half of our input voltage—we would need both resistors to be the same.

A more explicit way of stating this is with an equation. Given a starting voltage VIN connected to the first resistor, R1, and the second resistor (R2) connected to ground, the output voltage (VOUT ) coming out between the resistors will be given by the equation
$$ {V}_{OUT}={V}_{IN}ast frac{R_2}{R_1+{R}_2} $$
(9.1)

Note that the specific resistance values don’t matter yet—it is the ratio we are concerned about so far. To get 4.5 V, we can use two 1 kΩ resistors, two 200 Ω resistors, or two 100 kΩ resistors. As long as the values are the same, we will divide the voltage in half.

If we wanted an 8 V output, we would do a similar calculation. Since we start at 9 V, we need to use up $$ frac{1}{9} $$ of the voltage in the first resistor, and $$ frac{8}{9} $$ of the voltage in the second resistor. Therefore, our resistors need to be in similar ratio. We could use a 100 Ω resistor for the first resistor and an 800 Ω resistor for the second resistor. Alternatively, we could use a 10 Ω resistor for the first resistor and an 80 Ω resistor for the second resistor. It is the ratio that matters most.

9.3.3 Finding Resistor Values

So how do you determine exactly what value to use? Here is where we start thinking about the load again. While we have been treating the voltage divider as a series circuit, in truth we have one resistor in series and then a parallel circuit with the other voltage divider resistor in parallel with the load. Our simplified model (where we ignore the parallel resistance) will work, as long as the load resistance does not impact the total parallel resistance by a significant amount. Therefore, let’s look at how the load resistance affects the parallel resistance.

So, using Equation 7.2, we can write a formula for the total resistance of these two, with R2 being our second voltage divider resistor and RL being our load resistance:
$$ {R}_T=frac{1}{frac{1}{R_2}+frac{1}{R_L}} $$
Now, let’s look back at the circuit in Figure 9-5. Let’s say that the resistance of the load (RL) is 400 Ω, which is much less than the resistance of the voltage divider resistor (R2, which is 2,000 Ω). So what is the total resistance?
$$ {R}_T=frac{1}{frac{1}{R_2}+frac{1}{R_L}}=frac{1}{frac{1}{2,000}+frac{1}{400}}=frac{1}{0.0005+0.0025}=frac{1}{0.003}approx 333;Omega $$

This is significantly different from our simplified model which ignored the load resistance, which gave 2,000 Ω. That means that our simplified model won’t work with this value.

Now, let’s imagine a bigger load resistance so that it is equal to the R2 resistance (2,000 Ω) and recalculate:
$$ {R}_T=frac{1}{frac{1}{R_2}+frac{1}{R_L}}=frac{1}{frac{1}{2,000}+frac{1}{2,000}}=frac{1}{0.0005+0.0005}=frac{1}{0.001}approx 1,000;Omega $$
This is still significantly off, but it is much closer. So, now, let’s look at what happens if the load resistance is double of R2, or 4,000 Ω:
$$ {R}_T=frac{1}{frac{1}{R_2}+frac{1}{R_L}}=frac{1}{frac{1}{2,000}+frac{1}{4,000}}=frac{1}{0.0005+0.00025}=frac{1}{0.00075}approx 1,333;Omega $$
Here, we are getting much closer to our original value. Now, let’s say that the load is ten times the resistance of our R2 resistor, or 20,000 Ω. That gives us this:
$$ {R}_T=frac{1}{frac{1}{R_2}+frac{1}{R_L}}=frac{1}{frac{1}{2,000}+frac{1}{20,000}}=frac{1}{0.0005+0.00005}=frac{1}{0.00055}approx 1,818;Omega $$

This is very close to the resistance of R2 by itself. So what we can say is that our voltage divider circuit can ignore the resistance of the load if the resistance of the load is significantly more than the resistance of the voltage divider resistor. A way of writing this down is that RL » R2. What “significantly” means depends on how sensitive your circuit is to voltage changes, but, generally (and for the purposes of the exercises), I will say that “significantly more” should mean at least ten times as much.

9.3.4 General Considerations

So, for low-resistance loads, a voltage divider does not work well, because it puts too little resistance between the voltage source and ground. However, in Chapter 11, we will see that many circuits have loads of approximately infinite resistance, so voltage dividers work really well in those cases.

In general terms, a voltage divider with smaller resistors is “stiffer” because it varies less in response to variations in a load, but it also eats up more current. A voltage divider with larger resistors doesn’t work with low-resistance loads, but it also uses up much less current.

If you need to know full equations for figuring out voltage divider resistors, I have them listed in Equations 9.2 and 9.3. In these equations, VIN is the voltage coming into the voltage divider, VOUT is the voltage going out of the divider into your load, and RL is the load resistance. R1 is the resistor connected to the positive power supply, and R2 is the resistor connected to the ground. If you are good at algebra, you might see if you can deduce these formulas yourself from the information given in this section:
$$ {R}_2=frac{R_L}{10} $$
(9.2)
$$ {R}_1=frac{R_2ast left({V}_{IN}-{V}_{OUT}
ight);}{V_{OUT}} $$
(9.3)

9.4 The Pull-Up Resistor

The pull-up resistor is a strange circuit, but we will find very good applications for it once we start dealing with ICs in Chapter 11. It is probably easiest to describe by simply showing you a circuit and then describing how it works.

Figure 9-6 shows the circuit diagram for a basic pull-up resistor circuit. Normally, we think of lighting up an LED by pushing the button. However, in this case, pushing the button causes the current to bypass the LED, which turns it off.
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Figure 9-6

Basic Pull-Up Resistor

If you look at the path from where the circuit branches, when the button is not pressed, the current can only go one way—through the LED. However, when the button is pressed, the electricity has two options—either through the LED or directly to ground through the button. The electricity would always rather go directly to ground rather than through an intermediary, so all of the current goes through the closed button, and none of it goes through the LED.

Since the branch point is directly connected to ground when the button is pushed, that means that the voltage at the branch point is also zero. Kirchhoff’s voltage law says that no matter what path is taken, the voltage drop will always be the same. However, an LED induces a voltage drop, but the voltages on both sides of the LED are zero. Therefore, electricity cannot flow through the LED.

So what is the function of the resistor? The resistor connects the switch and the LED to the positive voltage source and provides a limitation on the current that runs through it. The resistor must be before the branch point for it to work.

Think about what happens without the resistor or if the resistor is after the branch point. The electricity will have a path directly from the positive voltage source to ground with no resistance—in other words, a short circuit. This will draw an enormous amount of electricity. Figure 9-7 shows what this would look like. Notice that when the button is pushed, you can trace a path from the positive voltage source to ground with no intervening resistance.
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Figure 9-7

Incorrect Way to Wire the Circuit

The resistor is called a pull-up resistor because it is connected to the positive voltage source and is used to “pull up” the voltage on the circuit to a positive value when the switch is open while still providing safety (by limiting the current) when the switch is closed.

In short, a pull-up resistor is usually used to supply positive voltage to a circuit which might be turned off by redirecting the voltage to ground. The resistor provides both the electrical connection to the positive source and a limit to the amount of current that will flow if the current flow is then routed to ground (usually through some kind of switching mechanism).

9.5 Pull-Down Resistors

One more basic resistor circuit that is often used is the pull-down resistor. While the pull-up resistor is connected to the positive power rail, the pull-down resistor is instead connected to ground. So, in a pull-up resistor, if part of the circuit is disconnected, the voltage goes high. In a pull-down resistor, if part of the circuit is disconnected, the voltage goes low. However, we don’t yet have enough background really to understand how they are used here. They are covered more fully in Chapter 12. They are merely mentioned here because they are one of the basic resistor circuit patterns that are seen throughout electronics.

9.6 Review

In this chapter, we learned the following:
  1. 1.

    Buttons and switches allow circuits to be altered while they are running by connecting circuits (allowing pathways for electric current) and disconnecting circuits (blocking pathways for electric current).

     
  2. 2.

    Most circuits are a combination of common, well-understood circuit patterns.

     
  3. 3.

    The more experienced you are with the basic circuit patterns, the easier it is to see these circuit patterns when you look at a schematic drawing.

     
  4. 4.

    A current-limiting resistor is a resistor that is used to limit the maximum current flow within a circuit, either to protect other components or to limit overall current usage.

     
  5. 5.

    A voltage divider is a pair of two resistors connected in series with one another (usually connected to a positive voltage on one side and the ground on the other), but with another wire coming out in between them to provide voltage to another circuit (called the load ).

     
  6. 6.

    In a voltage divider, it is assumed that the resistance of the load is significantly more than (i.e., greater than ten times) the resistance of the second half of the voltage divider because then the load can be basically ignored for calculating voltage drops.

     
  7. 7.

    For a voltage divider, the ratio of the voltages consumed by each resistor is the same as the ratio of their resistances. The output voltage coming out of the first resistor is the level of the voltage that will be supplied to the load.

     
  8. 8.

    Another way of stating the output voltage is $$ {V}_{OUT}={V}_{IN}ast frac{R_2;}{R_1+{R}_2} $$, where R1 is the resistor connected to the positive voltage and R2 is the resistor connected to ground.

     
  9. 9.

    Voltage dividers with smaller resistances are “stiffer”—they are impacted less by the resistance of the load. Voltage dividers with larger resistances are not as stiff but waste much less current.

     
  10. 10.

    A pull-up resistor circuit is a circuit in which a positive voltage which may be switched to ground at some point is provided through a resistor.

     
  11. 11.

    The pull-up resistor both (a) connects the circuit to the positive voltage to supply a positive current when the circuit is not switched to ground and (b) limits the current going to ground (i.e., prevents a short circuit) when the output is switched to ground.

     
  12. 12.

    It is called a pull-up resistor because it pulls the voltage up when the circuit is not switched to ground.

     

9.7 Apply What You Have Learned

  1. 1.

    In Figure 9-3, calculate the amount of current used by the whole circuit for each configuration of the switches S2 and S3 when S1 is closed. You can assume that the LEDs are red LEDs.

     
  2. 2.

    Build the circuit given in Figure 9-3 (you may swap out resistors with different but similar values—anything from 300 Ω to about 5 kΩ should work).

     
  3. 3.

    Given a 15 V voltage supply, what size of a resistor would be needed to make sure that a circuit never went over 18 mA?

     
  4. 4.

    Given a 9 V battery source, design a voltage divider that will output 7 V to a load that has a resistance of 10 kΩ.

     
  5. 5.

    Given a 3 V battery source, design a voltage divider that will output 1.5 V to a load that has a resistance of 1 kΩ.

     
  6. 6.

    In Figure 9-6, how much current is going through the circuit when the switch is open? How much when it is closed? You can assume that the LED is a red LED.

     
  7. 7.

    How would you modify the circuit in Figure 9-6 to keep the maximum current in the circuit under 2 mA? Draw the full circuit out yourself.

     
  8. 8.

    Build the circuit you designed in the previous question. If you do not have the right resistor values, use the closest ones you have.

     
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