## HomeExperimentsSpeed of Light

This project was motivated by the fact that RF frequencies about 1 GHz have become meanwhile a common application in daily life and the RF equipment has become quite affordable. Radio waves at this frequency have a wavelength of about 30 cm which makes them quite easy to handle.

If the wavelength $$\lambda$$ of a wave generated by an oscillator with a known frequency $$f$$ can be determined, the following formula $$\lambda = \frac{c}{f}$$, with $$c$$ as propagation velocity of the wave. From this it is easy to derive the value of $$c$$ from the measurement data:

$$c = \lambda f$$

Lets assume that we will be able to generate a frequency with an accuracy of 10 KHz and to determine a wave length down to 0.1 mm. This leads to an absolute accuracy of: Δc = Δλ ν + λ Δν = 0.0001m 1700 Mhz + 0.20 m 0.01 Mhz = 170 km/sec

## The Oscillator

The oscillator is build from an VCO and an LMX2364 PLL as shown in fig. 1.

 Fig. 1 -  PLL based RF generator. The LMX2364 chip provides the PLL; the LTC1063 filters the error signal and provides the feedback to the VCO which generates the final RF signal. The PLL can be tuned via the SPI interface with a precision of 100K in the range from 1.2GHz upto 1.8 Ghz.

The oscillator is connected to an micro controler PIC18F4500 via the data lines of the LMX2384 chip.

## Setup

The experimental setup is shown in figure 2. It consists of the previously desctibed RF generator and a  with so called Lecher line where the steady wave for a given frequency is expected to be created.

 Fig. 2 - Complete Setup

A lecher line comprises of two parallel lines, one connected to the RF generator an another line connected to ground (see fig. 3). Depending on the position of the short circuit between RF and ground line a steady wave can develop.

 Fig. 3 - Lecher Line setup

The concept of the experiment is to create a steady wave for a fixed frequency by moving the short circuit until the steady wave is measurable. Then to measure the wave length by measuring the voltage along the line.

This is done by means of the motor shown in figure 1.2 which moves a detector along the line under the control of the experiment controller.

On the other side of the axis a position detector is installed which allow to count the revolutions of the axis. Each revolution of the axis is triggering a measurement of the voltage. The revolution number is an direct indication of the current position of the detector.

## Measurements

The tricky part of the experiment is to create a steady wave for a given frequency by moving the short circuit into the right position. A typical example is shown below:

 Fig. 4 - This figure shows the measured voltage along the lecher line (red) .

The periodic signal in Fig. 4 does not meet the expectation of a sinusoidal steady wave. Most likely the signal is composed of two or more different waves created at different apertures in the setup; e.g. connectors. In order to select the best measurement the Fourier transform of the data (see Figure 5) is taken into consideration.

 Fig. 5 - Fourier transform of the data shown in figure 4.

## Summary

The tricky part is to identify a steady wave which is not a sum of several waves. From the catalogue of the actual measurements the selection of applicable measurements has to be done manually based on the Fourier spectra of these measurements assuring that a pure harmonic steady wave is taken as a basis.

 Frequency [MHz] Calculated [km/s] 1700 294867.68 1730 309708.28 1740 308484.60 1750 296835.00 302473.89

sThe average of different measurements is leading to 302473 km/sec which is higher then the speed of light in vacuum of 299792.458 km/sec.