*Part of a blog series *__Tube Amplifier Circuits Explained__

**Resistors**

You are likely familiar with a basic resistor: a device that intentionally holds back current and is rated in Ohms. I won’t go over these in much detail other than to mention briefly a few types of resistors and to cover wattage ratings.

Resistors are made in different ways and you’ll see them categorized—metal film resistors, carbon film resistors, carbon composition resistors, wirewound resistors, etc. There are simply different ways to construct a resistor for varying objectives and you end up with different attributes, sizes, costs, etc. In my amplifiers I use metal film resistors and wirewound resistors, which tend to have the lowest noise. Noise is an unwanted side effect of a resistor that impacts the signal passing through it. It can be thermal noise, or current noise caused by the structure of the resistive material when current runs through it. While we want to minimize noise, this is not in my opinion the largest problem we need to deal with compared to many other aspects of circuit design and selection of high-quality components such as tubes and transformers. Resistors are relatively inexpensive components and have a pretty easy job to do if selected and rated properly.

Note that wirewound resistors are generally available in relatively lower resistances due to their method of construction. I use them typically for cathode bias resistors, which are often less than 1 kOhm. Wirewound resistors can be inductive, but in this application, it will not have a noticeable impact.

Resistors are manufactured with a power rating—1/2 watt, 1 watt, 2 watts, 5 watts, etc. As voltage is forcing current through a resistor, electrical power is converted to heat energy. The resistor is designed to handle a maximum amount of power before it is destroyed by too much heat—if you’ve ever made a mistake in a circuit, you will know you can easily burn up a resistor! Consider a circuit that has 100V causing 8mA of current to flow through a resistor that is 12.5kOhms (Ohms law validates these relationships). The power dissipated will be 0.8 watts (P = IV). So you would need at least a 1W resistor to handle this power. But a good rule of thumb is to use a resistor rated for double the power your circuit needs. I would select a 2W resistor in this case. There is no problem using an overrated resistor, other than cost and size. I often use 2W resistors even when power required is much lower because I buy them in bulk and they are physically larger than tiny ¼ or ½ watt resistors and my fingers can work with them better!

**Capacitors**

A capacitor stores energy in an electric field. It can be created in various ways, but commonly is done using two conductors (or plates) separated in some way, such as by a film or ceramic material or dielectric. There is no electrical connection between the two conductors, but because they are physically close, a voltage potential between them causes a positive charge to build up on one plate and a negative charge on the other. The physical characteristics of the capacitor determine how much energy can be stored in this way, and we measure capacitance using Farads, or more commonly microfarads (µF or uF), which are one millionth of a Farad.

Since there is no electrical connection, capacitors do not allow DC to pass through them. But a change in voltage will cause the plates to charge or discharge, allowing current to flow across the capacitor, so AC, as it changes rapidly from positive to negative, will pass across a capacitor. This is an important principle: the current in a capacitor is directly related to the rate of change in voltage—a very slow-changing or steady voltage will have low or no current, while a very fast change in voltage will have higher current. We can quantify the action of a capacitor to oppose lower frequency voltage changes using Ohms, the same unit of measure we use for resistance. But in this case we would refer to it as **capacitive reactance** (Xc)**. **I promise I won’t use many formulas, but you might find it helpful to see how we can calculate the reactance of a capacitor, since it will vary based on frequency (f) and capacitance (C):

Xc = 1 / (2πfC)

For example, a capacitor that is 33uF in capacitance that has an AC voltage at 120Hz across its conductors would have about 40 Ohms of reactance at that frequency. What would you guess is the reactance at a lower frequency, like 60Hz? Yes, lower frequencies would have lower current passing, so it’s a higher reactance of 80 Ohms. How about a very high audio frequency, like 8kHz? Plug that into the formula and you’ll see the capacitor would present only about 0.6 Ohms of reactance. Cool, huh? And very useful! Visualized here is a plot of a 33uF capacitor’s reactance at various frequencies.

One more example, let’s see how this reactance changes based on higher and lower capacitance. Imagine this was a bigger capacitor of 150uF instead of 33. Now, because the capacitor can hold a greater charge, those same frequencies we just looked at have different reactance: 120Hz would have reactance of only 8.8 Ohms and 8kHz would have reactance of 0.13 Ohms. So a higher capacitance will lower the reactance at a given frequency.

Capacitors are rated for a certain voltage, and many are not manufactured with high precision in capacitance, often +/- 20%. Higher voltage rating and capacitance will require a physically larger (and usually more expensive) capacitor. Always choose a capacitor with a higher voltage rating than you expect it to see in the circuit. Exceeding the voltage rating will lead to the failure of the capacitor.

Capacitors, like resistors, come in a variety of types. For high voltage and capacitance values, we typically need to use electrolytic capacitors. These have a few drawbacks in terms of lifespan and some characteristics, but are still our best choice. Most electrolytics are polarized, so you must wire the negative side to the lower voltage potential or it can be destroyed or even explode. Electrolytic capacitors have a liquid inside of them and are sensitive to high temperatures and “ripple current” that can create internal heating of the capacitor, shortening the life if not rated sufficiently for the application.

In some cases when we have smaller capacitance needs, we can use some type of film capacitors. These are better for certain audio purposes than electrolytic capacitors, but would be too large physically for other uses when capacitance needs to be higher. You’ll see in this circuit explanation that we use a film capacitor for coupling between the stages of amplification—a sensitive part of the circuit where we don’t need much capacitance and want a high quality component to preserve the purity of the signal. Audiophiles love fancy coupling capacitors and you can find some for outrageous prices, probably made by elves using ingredients that cost many gold coins and precious gems. I believe in good caps, but only so far, like most things.

**Inductors**

Inductors (some called “chokes”) also store energy, but instead of an electric field as in a capacitor, it is stored in a magnetic field. These are usually made of some type of insulated wire that is wound into a coil, sometimes around an iron core. When current flows through the coil, a magnetic field is created. We can measure “inductance” with a unit called Henries (commonly using the symbol L) and it is based on number of turns of the wire, length and cross-sectional area and core material.

Under DC conditions through an inductor, current flows and a magnetic field is created. At this point, the inductor acts as though it were a short-circuit, with the only resistance being the natural resistance that the coiled length of wire would have.

However, when there is AC, the current is trying to change rapidly from one moment to the next. But when energy is built up in the magnetic field from increasing current, the inductor will tend to maintain that same level of energy, which is related to the amount of current. Think of it a bit like momentum and inertia: something put in motion will tend to continue in that same motion, or something not in motion will tend to stay not in motion. So when the current rapidly changes, the inductor resists the change. The net effect of this is that the inductor forms a voltage between its two connectors in opposite polarity to the change in current.

I know, this requires some heavy thinking, physics, force fields, ESP, and Jedi training to really get the theory of it, and I have not explained it with much depth. But the main takeaway is that inductors resist changes in current, and the voltage across the inductor is proportional to the rate of change of current. This is exactly the opposite of a capacitor, where current is related to the rate of change of voltage. Inductors have “reactance” similar to capacitors, that varies based on frequency. Higher frequencies will have greater inductive reactance than lower frequencies. The inductive reactance (XL), measured in ohms, based on frequency (f) and inductance (L) is:

XL =2πfL

You will see an inductor (choke) and capacitors in this amplifier circuit performing important roles of blocking or allowing DC or AC, or filtering a power source to remove ripples in the voltage or current. I’m not touching on many other aspects of these components, including how phase of AC is altered by these components, but hopefully this gives some of the basics to understand our circuit.

**Transformers**

A transformer also uses principles of magnetic induction. Two coils of insulated wire can be wound on a core. When a voltage is put across one of the coils (the “primary” side of the transformer), it will magnetize the core and induce a voltage onto the other “secondary” coil. The two coils can have a different number of turns, and the ratio of these turns will result in a higher or lower voltage on the secondary side. This is very useful when we want to “transform” a voltage from one level to another. We use this in two places in an amplifier: to convert household mains voltage from 120V AC (US) to some higher voltage needed in the amplifier circuit, and also after amplification to convert from a high voltage signal down to a low voltage usable for speaker outputs.

A transformer works with AC only. There is no electrical connection from primary to secondary, and DC would pass across the primary side as a short circuit (possibly damaging it). Remember how the inductor resists changes in current and will create a voltage to try and maintain its state of magnetic field? Under AC voltage conditions on the primary, a voltage will be created by the transformer on the secondary side as an inductive response, with current in opposite direction to the primary.

Keep in mind that this is a passive electrical activity (unlike an amplification process). We are putting the circuit load on the secondary side of the transformer where there is going to be a voltage, load resistance and resulting current draw. On the primary side, that load will appear differently due to the turns ratio so the current will also be different. If for example, a transformer has a 1:4 primary to secondary turns ratio, then voltage will transform from 120V on the primary to 480V on the secondary. A load on the secondary that results in a current draw of 100mA would have that current appear on the primary side using an inverse ratio as a draw of 400mA of current.

All that said, this is a simplified view and a transformer is not perfect, there are some losses in efficiency in several ways we won’t discuss. Some power is dissipated as heat, and a power transformer can therefore become hot under a full load, and is typically designed and rated to allow for this.

Next: We are ready to look at the __Big Picture of the Circuit__ for our example.

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