In today's video we're going to plunge into the mesmerizing world of early radio technology through the assembly and analysis of a DIY spark gap transmitter. I'm going to walk you through the schematic, the theory behind operation, the testing and characterization of the operational circuit, and of course I'm going to show you what the received signal sounds like. The circuit itself is extremely simple. It consists out of an RC charge circuit, of course the spark gap itself, and a resonant LC tank circuit. Three millimeter acrylic glass is used to house the entire construction. The RC charge circuit consisting out of R1 and C1 is responsible for controlling the spark gap's triggering frequency. After applying the supply voltage, the voltage across C1 is determined by this exponential equation, where Vc1 is the voltage across C1, V in is the supply voltage applied to the circuit, T is the time in seconds, and R1 times C1 is also called the time constant, in this case 10 milliseconds. This time dependence provides a straightforward method for modifying the spark gap's triggering frequency. Increasing the supply voltage increases the firing rate of the spark gap and reducing the supply voltage reduces the firing rate accordingly. Controlling the triggering frequency is an important feature as it directly relates to the pitch of the tone received in an AM receiver. A spark gap transmitter obviously requires a spark gap. Its main purpose is to dump the accumulated charge from C1 into the tank circuit at a controlled rate. The spark gap itself was constructed from carriage bolts and a few pieces of acrylic glass. Assuming an idealized marginous field and an electrode spacing of 10mm, the breakdown voltage of air is around 3kV permm. While this rule of thumb is certainly precise enough for this experiment, I would just like to point out that in reality the exact breakdown voltage depends on a lot of parameters such as temperature, humidity, and the exact gas mixture. Lastly, there's the resonant LC tank circuit consisting out of C2 and L1. The component values used in this demonstration should yield a resonant frequency close to about 3MHz. L1 is a handmade 8-turn air-core inductor wound from enameled copper wire with a tap 1.5 windings from the ground to connect an antenna or siloscope probe. Overall the operation of the circuit can be summarized as follows. When the supply voltage is applied, the charge circuit R1 and C1 charge up until the breakdown voltage of the spark gap is reached. The breakdown of the spark gap allows for energy to flow into the LC resonant tank circuit which in turn generates a strongly damped signal on the desired resonant frequency. A quick functional test confirms that the circuit operates as intended. Before I move on to analyzing the resulting waveform, let's listen to what the signal sounds like on an AM receiver. Increasing the supply voltage also increases the pitch of the received tone. Capturing the generated waveform within a siloscope confirms the generation of a signal with a frequency of around 3MHz. The amplitude envelope of the generated signal follows a quick exponential decay. This general equation for characterizing damped harmonic oscillators, be it a spring, a pendulum or an LC tank circuit, can be used to describe the output waveform. V of T is the output voltage at time T, A the initial amplitude, delta the decay rate, omega the angular frequency, and T the time in seconds since the spark gap has last fired. The decay rate delta can be calculated by dividing the logarithmic decrement lambda through the time period of the oscillation. Calculating the logarithmic decrement requires noting the amplitude A of in successive oscillations, ignoring the first 1.5 cycles of the output signal for reasons I'll get into later. The amplitudes are noted down as 266 volts for the first peak. The second peak is at 174 volts, and the consequent peaks are at 126 volts, 96 volts, 72 volts, and 52 volts. The cycle duration and the actual frequency of oscillation can also be read directly from the oscilloscope screen. By plugging those measurements into the equations, we can now calculate the logarithmic decrement as well as the decay rate. Plugging the initial amplitude of 266 volts, the decay rate we just calculated, as well as the measured frequency, into the equation, yields an equation that mathematically expresses the output of the spark gap transmitter. Comparing the graph of the function with the actual measurements shows that they are very similar, at least, and certainly good enough for government work. To investigate the higher frequency oscillation at the beginning of the waveform, that I so far chose to ignore, let's take a look at the spectrum of the output waveform. At first glance, it appears that there's only a single peak at a center frequency of the expected three megahertz. Even though this peak is extremely wide, there seems to be nothing out of the ordinary. However, increasing the span paints a completely different picture. While the three megahertz peak is certainly the strongest, there now appears a second peak at around 10 megahertz as well. The source of this design flaw is as in many cases this nasty thing called reality. The problem is that the moment the spark gap is triggered, C1 is fully charged and C2 is empty. Initially, the fully charged C1 alone interacts with L1, with C2's contribution to the oscillation delayed. Due to the extremely large bandwidth of this transmitter and certain legal restrictions, this transmitter isn't good for anything other than demonstrations anyway. So therefore, I have no intentions of fixing this design flaw. Speaking of bandwidth, we can also calculate the quality factor Q by first calculating the damping ratio Zeta from the logarithmic decrement lambda, which we previously calculated. Clugging all known values into the equations yields a numerical Q factor of 11.56. At a frequency of three megahertz, this corresponds to a half-power bandwidth of approximately 260 kilohertz, which seems to align reasonably well enough with the FFT spectrum.