How To Choose A Resistor

How do we choose the right resistor when designing and building an electronic circuit? Here are the major parameters that should be kept into account.

bunch_of_resistors

A resistor is a component made out of a poor conducting material, so that it can offer a resistance to the flow of the current.

You can think to resistance in terms of the obstacles that charges encounter when moving from one end to the other of a conductor. The more obstacles, the higher the resistance. In a metallic wire, for example, the charges are the electrons of the conduction band (see this post and this other one for further details).

In today’s post I would like to address an issue that sometimes is underestimated when designing an electronic circuit: how to choose the right resistor for the job.

Resistors are not all the same. Besides the resistance value that distinguishes one from the other, there are other factors that are important as well.

Here is a list of all the important factors, why they are important, and what are the consequences of not choosing a resistor based on each specific factor.

  • The first thing that comes to mind is the tolerance, which is usually provided on the body of the resistor itself, along with its resistance value.

resistor_color_bands

In color coded resistors, the tolerance is defined by the band that is far away from all the others. In the above picture, for example, it is the gold band, which means that the tolerance is of 5%. In other resistors, where the resistance is explicitly written on the body of the resistor, the tolerance is usually written in clear along with the resistance. More in general, you’ll have to refer to the data sheet provided by the constructor to figure out its tolerance.
Tolerance is an important factor for those circuits that require very precise resistors, like measuring instruments and the like. It is also important when the resistor is used for the polarization of a critical component. If the resistors used in the project have a tolerance that is too high, the whole circuit may not function properly because the actual value of the resistor is too different from the one that was required.

  • Operating Temperature. This depends both from the ambient conditions and by the temperature raise produced by the power dissipation. There are two reasons to keep the temperature range into account. First, resistors slightly change their resistance with the change of the temperature. Using the resistor outside its temperature range would cause a variation greater than the one considered by the tolerance. Second, but not last, when the resistor is traversed by current it heats up. As long as the current stays within a range for which the power dissipation is not exceeded, everything is fine. Otherwise, the resistor can easily overheat and burn.

scorched_resistor

  • Maximum Voltage. Operating a resistor above its maximum voltage rating may cause sparks that would destroy the resistor.

burned_resistor

Resistors used in low power circuits usually have a maximum voltage in the order of at least 100V, and that’s why people usually don’t care or it doesn’t even know that there is such a parameter. In fact, low voltage circuits will normally never exceed the maximum voltage of any resistor. However, there are specific applications where voltages in the circuits can be above the 100V threshold. In such cases, it is important to verify that the resistors used in the circuit can withstand those voltages.

  • Temperature coefficient. This is the parameter that tells us how much the resistance changes per degree Celsius. It depends on the material the resistor is made of, but also on the heat dissipation capability of the component. Some resistors are built with an embedded heat sink to reduce the value of this factor.

power_resistor

This information becomes important in those cases where it is known that the resistor is going to dissipate a considerable amount of power. Based on that, it is possible to figure out if the resistor needs an external heat sink and, eventually, the heat sink thermal resistance.

  • Parasitic Capacitance and Inductance. A real resistor does not have only a resistance but also a very low value of capacity and inductance that may affect its functionality at high frequencies.

equivalent_resistor

These parasitic capacitance and inductance are caused by the physical dimensions and shape of the component and cannot be avoided. When working at high frequencies, these values need to be taken into account, since they will generate both capacitive and inductive reactance that will affect the value of the resistor at the particular frequency it is going to be used.

  • Packaging. This keeps into account where and how the resistor is going to be mounted. It can be a through holes resistor, which is provided with two leads to make the connections. The leads are usually inserted in the holes of a perforated board or of a Printed Circuit Board (PCB). Or, the resistor can be a Surface Mounted one. This has no wires, just two pads that can be directly soldered on a Surface Mounted technology (SMT) PCB. Other factors affecting the packaging include the possibility of attaching it to an external heat sink, and/or the necessity to properly ventilate it, to guarantee enough heat dissipation.

 

More on the Theremin: The Heterodyne Mixer

The heterodyne mixer is the stage of the Theremin where the high frequency signals coming from the pitch reference oscillator and the pitch variable oscillator are combined together to obtain the audio signal.

mixer

Here we are again with another post about the Theremin, which can be considered the first electronic musical instrument ever invented, almost 100 years ago, in 1919, by the Russian physicist Leon Theremin.

At that time the Theremin was made out of thermionic valves and used a lot of space and electric power.

theremin_in_concert

Today, thanks to the evolution of electronics in the last century, we can make one that can occupy much less space while also consuming much less power. In fact, this is one of several articles that I have already published on the design and construction of such musical instruments, using solid state components.

Please consult this site archives for the previous articles on the subject and THIS link for schematics and diagrams, which I keep updating as I go in designing and building the pieces of the instrument

A corresponding series on the Theremin is also available on YouTube at THIS link. There, I describe every detail of my project, explaining how the various parts of the device work and how I built everything so far in a very inexpensive way.

In this article I will explore the Mixer stage of the Theremin, describing how it works and how it is used within the Theremin itself.

The mixer is the Theremin stage that combines together the signals from the pitch variable oscillator and the pitch reference oscillator, to create an audio signal that is essentially the sound that the Theremin produces.

The combination of the two input signals is done with a process called heterodyne. It basically consists in multiplying the two input signals by exploiting the non-linear characteristic of transistor Q1, which is carefully polarized outside its linear zone. The result of the multiplication is a new complex signal containing frequencies that are the sum and the difference of the frequencies of the original input signals. Since the frequencies of those input signals are close to each other, their difference falls in the audible range, which is what produces the peculiar sound of the instrument.

Looking at the schematic, you can see that the two input signals are mixed together at the base of transistor Q1, which they reach passing through capacitors C4 and C8, used to decouple the mixer from the direct current superimposed to the input signals.

Transistor Q1 is polarized in the non-linear zone of its characteristics. Because of the non-linearity of the transistor, the two signals end up being multiplied with each other, producing a new, more complex, signal that contains both the sum and the difference of the frequencies of the input signals. This heterodyne process, therefore, applies the following equation to the two input signals:

sin(2πf1t) * sin(2πf2t) = 1/2 cos(2πf1t – 2πf2t) – 1/2 cos(2πf1t + 2πf2t)

where the factors on the left side represent the two sinusoidal input signals, and the resulting complex signal is on the right side of the equation. The above formula is actually a simplification, because it does not take into account the phase shift between the two input signals, which should appear as a phase factor in the parameters of each of the sine waves on the left side of the equation. However, if we did the full calculations, we would see that we would still obtain the same output waves, but each would have an extra amplitude factor that depends on the initial amplitude of the input signals and on their phase shifts.

Anyway, the complex signal obtained at the collector of transistor Q1 is supplied to a Low Pass filter, made up of the components R4, R7, R8, R9, C2, C3, C5, C6 and C7. The filter produces an attenuation of the high frequency element of the complex signal, effectively leaving only the one at low frequency  cos(2πf1t – 2πf2t), which is the audio signal.

That output signal is then passed to the next stage of the Theremin, the VCA, where it acquires the dynamics of the music sound. We will talk about the VCA in a future post.

If you are interested in more information on the Theremin Mixer and how I built it, please watch this companion VIDEO on YouTube.

And, as always,

Happy experiments !!!

An LED Bar Graph VU Meter

VUmeter

Bar graphs VU meters can be easily made with a simple integrated circuit. There are several of them with different characteristics, but they all present the same basic functionality: one or more LED in a row are used to visualize, more or less precisely, the voltage amplitude presented to the input. That voltage can be either a direct current or an alternate current and, in particular, it could be the output of an audio amplifier.

But, what is inside these integrated circuits? How do they make possible this kind of behavior?

Here is the design of a simple gadget that shows how a bar graph VU meter works. Building and using this device is certainly a fun way to learn the principles used to design the bar graph integrated circuits.

bar_graph_vu_meter

The basic element of the circuit is the one made with the components Q1, R1, R10, D1, and D10.

This block of components then replicates several times to increase the number of LEDs used in the bar graph. In this particular case, the same circuit is replicated 8 more times, for a total of 9 LEDs in the bar.

You can also see that each block, or stage, receives as the input the output from the previous stage.

Diodes form D10 to D17 are used to provide a different threshold to each stage. In fact, let’s say that the first stage is triggered when the voltage on the anode of D10 reaches about 3V. In order to trigger the second stage we will need 3V on that stage, but that means that the voltage at the first stage has to go up to 3+0.6V, or 3.6V. The extra 0.6V is the forward voltage of diode D10.

Similarly, to reach each further stage, we will need an input voltage 0.6V higher for each stage we want to light up.

In the end, to light up the last stage we will need an input voltage of at least 3 + 8 times 0.6V, or 7.8 volts.

Once the threshold is reached in a stage, the corresponding transistor switches on and starts conducting a current that is only limited by the LED and the series resistor which, in this case, is 330 ohms. With the values in the circuit, the LED current will be about 20 mA.

So, when we apply a voltage to the input terminals, depending how high the voltage is we will see a number of consecutive LEDs lighting up, while the remaining will stay off because their respective stages have not been triggered yet or, in other words, the voltage at those stages hasn’t yet reached the threshold imposed by the diodes.

Note also that resistors R10 to R18 are not all of the same value. This is because by the time the voltage reaches the threshold in the last stage with transistor Q9, the voltage on the previous transistors is higher and higher while we move to the left of the circuit, since we need to add back the 0.6V that the diodes are dropping. Therefore, to avoid damage to the transistors on the left, we need to increase the base resistor when moving from the right to the left of the circuit.

Another thing to notice is the trimpot located at the connectors for the input signal. The circuit as it is, is capable of handling signals up to the value of the power supply, which is 9V.

However, we can adjust the trimpot to handle higher signals, just by moving the trimpot cursor toward the end that is connected to ground, in order to get only a fraction of the actual input signal.

Conversely, if you had a very small input signal, that could not trigger even the first stage of this circuit. In that case, you could still add a very simple amplifier between the source of the signal and the input of this circuit, which would help increase the level of the signal to the required value.

Finally, you see that the bar graph meter is powered with a 9V power supply. I used such value so you can use a 9V battery, if you like to try the circuit.

However, if you wanted to use this circuit as part of a more complex system having a higher value of the power supply, you could just modify resistors from R1 to R9 and use the power supply of that system.

For example, if you planned to use 12V instead of 9, you would use resistors of 470 ohm rather than 330, and everything would work just fine.

Remember, however, that 9V is the minimum voltage you can use to correctly power the bar graph circuit. You can only increase the power supply voltage to a higher value and increase accordingly the resistors R1 to R9. That is because we need a power supply that exceeds the voltage at the base of the leftmost transistor Q1, which can be as high as 7.8 volts, as we said before.

The circuit can be easily assembled on a per-board, like in the case in the frnt picture of this post. There, I used a 3 prongs connector to provide the power supply and the input for the external signal.

Once the circuit is assembled, set the trimpot with the cursor toward the ground side, then power up the device and put a signal to its input. The signal should be the highest possible with the amplifier to which you are attaching the VU meter. Then, adjust the trimpot until all the LEDs are lighted up. Now the circuit is tuned and you can input to it any signal that changes between 0V and the max you used for the tuning.

For further information, and to see the VU meter in action, take a look at this video that I posted on my YouTube channel.

Happy experiments!!!

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