Tube Amplifiers Explained, Part 2: Core Concepts, Sound, Voltage & Ohm's Law
Updated: Mar 29, 2020
Part of a blog series Tube Amplifier Circuits Explained
What is sound?
Sound is a type of energy created by vibrations. When things collide or vibrate, there is a physical process that moves the air around those things, and sound travels through the air as pressure waves that compress and expand based on the vibration source. Eventually, these sound waves reach and vibrate within our ears, creating signals that our brain interprets as music, speech, or other noises.
This barely describes the phenomenon, but a key takeaway is that sound waves can be caused by vibrations that go fast (high pitch) or slow (low pitch), and that move a small amount (quiet) or a lot (loud). We can describe very basic sound waves using these characteristics—frequency and amplitude—and plot them on a chart.
Electronic audio recording equipment converts actual sound waves moving through the air into electric signals using a microphone that reacts to the sound waves creating a voltage at a frequency and level corresponding to the sound. A recording device can capture this stream of varying voltage information, representing the sound waves, saving it for later. A playback device can take the stored information, convert it to a voltage signal again, which is then amplified to a larger, more powerful signal. We then need a device to turn it back into sound waves in the air. This is the loudspeaker, often made using a cone that is vibrated magnetically and this physically moves the air to generate sound waves that a listener can hear. There is much more to this entire process and the physics of loudspeakers, but the important concept is to understand that an audio signal in our amplifier will be a voltage changing over time.
We have two ears that can each hear sound waves separately and interpret spacial location from them, and stereo recordings have two separate signals that are recorded or engineered, and eventually played back, one for each speaker to recreate a form of dimensional soundstage. In most cases through this manual, we will discuss a single process of audio amplification, but know that this process is duplicated, one for each channel (left and right).
Pure cycles of rising and falling amplitude over time are sine waves and can be described with math formulas that I won’t introduce here. But you could think about sine waves as a type of building block that, in complex combinations of frequency, duration and amplitude, can make up music or other audible sound. Combinations of multiple waves will add to a compound wave, as shown in a simple example here. This will be important when we start to discuss distortion and harmonics.
Humans can hear sound only within certain frequencies. To cover human hearing adequately, most audio equipment is designed or evaluated in the range between 20Hz and 20,000Hz. Hertz (Hz) is a measure of the number of wave cycles per second. A vibration at 20 cycles per second is very slow, and we would probably be feeling this very low “thunder” more than we really hear it. On the other hand, 20,000 is such a high pitch that most of us cannot even hear it—especially as we age or lose hearing from exposure to loud noise or bad marching bands. Although it is rare that a music recording spans 20Hz-20kHz or that a loudspeaker could accurately reproduce that wide of a frequency spectrum, we still will design, measure and expect our amplifier to be able to reproduce as accurately as possible this range of audio frequencies.
The charts of sine waves above (and visualized on an oscilloscope) are in the time domain, with frequency illustrated as the number of peaks and valleys over time on the horizontal axis. Another commonly used graph for audio measurements is in the frequency domain—a horizontal axis representing frequency from low to high, and the vertical showing a measurement of amplitude that a device may reproduce at each frequency.
The chart on the left here shows an example ideal flat frequency response that we might have with an amplifier: frequencies across the audible range of 20 – 20,000 Hz can be reproduced at an equal amplitude. The chart on the right shows an illustrative speaker frequency response—wow, it’s very choppy, huh? There are some peaks and valleys where some frequencies are reproduced louder than others. This is typical of a speaker, where a very flat response is difficult to achieve and involves a wide range of physical implications in the action of the speaker drivers (woofer, midrange, tweeter), crossover points where drivers are transitioning responsibility, diffraction of sound from the shape of the speaker, and many others. In fact, the listening room will have a high impact on how we perceive the sound due to reflections. There is an extensive field of study of loudspeakers, room treatment, and other areas—more fun for the DIY hobbyist to explore! Just note for now that the frequency response of your speakers is incredibly important in achieving high-quality sound. It could require large and often expensive speakers to have a flat frequency response and one that extends down to the lowest ranges around 50 Hz and below.
A common measurement unit for frequency response is decibels (dB), a non-linear unit to measure the intensity of sound relative to a reference. If the reference level of 0 dB represents the threshold of human hearing, then a normal conversation might be 60dB in intensity, while a loud music concert could be 100-120dB. It is on a logarithmic scale because our hearing responds differently to low intensity sounds than it does to high intensity ones: 0dB is near silence, 10dB would be 10 times as powerful, 20dB would be 100 times as powerful, 30dB is 1000 times as powerful, and so on. A rule of thumb is that a 10dB increase is perceived as twice as loud.
In both charts, near the bottom and the top ends you see the frequency response start to fall off. On a response chart, the roll-off point that reaches -3dB point relative to a normal level is referred to as the cutoff point, where calculated power at that point is technically half of the 0 dB reference point. Measuring a response that fluctuates within 1-3 dB might be considered flat with minimal perception of change, but more than that could start to become noticeable in listening. For example, a speaker that could reproduce a flat response across a range, but rolls off with a cutoff at 100 Hz means it is down 3dB at 100Hz relative to the maximum level. As the rolloff continues it might be down 10dB by 80Hz (or half the perceived loudness of the higher frequencies) and you might feel it sounds thin or lacking in bass because these frequencies are not loud enough relative to others.
Ohm’s Law: voltage, current and resistance
While it’s likely you know this already, it’s worth quickly highlighting the basics of a circuit: a closed loop involving voltage (V), the difference in electric charge from one point to another, current (I), the rate of change of electrical charge measured in Amperes (Amps), and resistance (R), which opposes the current flow and is measured in Ohms. These three are the foundation to understand how a circuit is operating. Some type of power source creates a voltage that is higher in one place in the circuit relative to another. This voltage, sometimes referred to using a concept of “pressure”, will force electrical charge to flow through the circuit as much as the resistance will allow, and this flow is measured as current. As current flows through the resistance, or the “load” of the circuit, the potential voltage drops until it is used up by the time the circuit is closed back to the power source.
We can use one of the greatest magical formulas ever, Ohm’s Law, which describes the relationship between these three (and we can solve for the third if we ever know the other two): Voltage (V) equals Current (I) times Resistance (R).
V = IR
I = V/R
R = V/I
In a direct current (DC) circuit, there is a source of positive charge and electricity flows in one direction. Perhaps the voltage source creates 12V DC, and the resistance in the circuit could be a simple resistor or could be some component that performs work when current is flowing, causing resistance or load on the circuit. In the example below, there is 12V of positive potential on one side of the battery, relative to the other side that closes the circuit. In between is a load that represents 3000 Ohms of resistance. Using Ohm’s law, we can calculate that this load will draw 0.004 Amps, or 4mA of current (I = V/R).
If there were no load, or no resistance, (essentially a short-circuit) then Ohm’s law would tell us there is 12V divided by 0 Ohms, or infinite current that would flow. This is obviously impossible in the real world, but we know that a short circuit will draw as much current as the power supply can provide, which could damage components, blow a fuse, etc.
You will notice I drew arrows in the direction from negative to positive to represent the current. Don’t worry about direction. There is a history and convention of thinking about current flowing from positive to negative, and we often refer to a “voltage drop” that happens across the load that makes us think about the starting point being higher and moving to a lower potential. Electrons actually move from negative to positive. Don’t let it tangle you up. It’s two sides of the same coin. The key point is that there is a difference in charge between the two points in the circuit, and the amount of resistance between those points, as well as the amount of difference in charge (voltage) determines how much current (rate of change) we have.
Our houses use alternating current (AC) as the power source because of limitations that make it difficult to transmit DC over long distances. Alternating current is a voltage that changes rapidly back and forth from positive to negative at some frequency. In our homes, we have 120V AC at 60 cycles per second (Hz).
A circuit can have a load that functions on AC, such as a light bulb. But in many cases, an electronic device will need to convert the alternating current into direct current for the circuit to operate. We will discuss this process later when we go over power supplies and rectification.
Sound waves discussed in the first core concept can also be represented as AC voltages changing over time positive and negative at various frequencies or complex AC waveforms.
AC introduces a question if we wish to perform some measurements or calculations. What is the actual voltage of an AC power source if it is continually changing? We need a few more ways to describe this voltage. Peak voltage is the highest positive voltage in the cycle, and peak-to-peak voltage is the difference from the highest to lowest point in the cycle (usually twice the peak voltage). RMS voltage (root mean square) is a way to measure this AC voltage and express it as an equivalent DC voltage that would produce the same power dissipation. (Some digital multimeters can measure RMS voltage while others use techniques that estimate it assuming an AC sine wave.) RMS voltage can be calculated by multiplying the peak voltage by 0.7071. So in your home, if you measure the voltage from a wall outlet, it may be 120V RMS, but the actual peak-to-peak voltage is about 340V.
Finally, while we are on the subject of Ohm’s law and the voltage and current through a resistive load: power (P) represents the rate that energy is produced or used in a circuit. It is measured in Watts and is the product of current times voltage (P = IV). Or, knowing Ohm’s law, you could calculate power knowing other combinations, such as resistance and voltage. For example, a circuit with 500 Ohms resistance and 24 volts of potential would dissipate 1.15 Watts of power. Hopefully this power is doing some useful work! Sometimes power may be transferred to heat energy.
Next: Additional Core Concepts about Common Components.