FP III Interferometers and filters with electrical waveguides

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1 FP III Interferometers and filters with electrical waveguides Version: 1. März 2013 Inhaltsverzeichnis 1 Task 1 2 Fundamentals Splitter impedance The experiment Spectrum analyzer Measuring the frequency Analyzing the spectrum Electromagnetic shielding, antenna Using the spectral analyzer as a receiver time domain measurements Reflexion wave velocity dispersion frequency-dependent signal transmission Damping velocity of propagation Reflection multi-path filter two-path filter path filter Simulation of multi-path filters Annotations material list Task The aim of this lab assignment is to learn how signals are guided through a cable, exemplified by electromagnetic waves in a coax cable. You will investigate both the generation, splitting and merging of signals as well as the influence of disturbances and their elimination. The electromagnetic signals will be verified both in the temporal and the spectral domain. The gained knowlegde is relevant when operating numerous measurement apparatus, and also in the field of data transmission. You will build up and test several filter circuits in the radio frequency range. These circuits are made of coax cables, impedance-matched splitters and attenuators. The frequency response is monitored using a spectral analysator and a tracking generator, while the temporal response is investigated using a pulse 1

2 generator and a fast oscilloscope. The experimental results will be compared to theoretical predictions obtained from numerical simulations. 2 Fundamentals In preparation for the lab, please inform yourself about the following terms and concepts of high-frequency technology: coaxial cable, wave impedance, impedance matching, input impedance, internal resistance, cable stub splitter, combiner, attenuator decibel (and its conversion to voltage and power ratios) Filters with finite impulse response FIR filters Filters with infinite duration impulse response IIR filters Fourier transform, sinc function oscilloscope; data sheet Hameg HM2005 : [1]. rf spectrum analyzer with tracking generator; data sheet Hameg HM : [2]. in connection with the spectral analyzer: VBW (video bandwidth), RBW (resolution bandwidth) The use of the following sources is recommended: [3, 4, 5]. 2.1 Splitter impedance Using a T-piece adapter signals can be split. The impedance of the two outputs of the T-piece adapter can be calculated by taking the two cable impedances in parallel: Z 0 = 50 Ω 50 Ω = 25 Ω. However, this value differs from the impedance at the input. Different impedances on the signal path lead to reflections. In our experiment, the provided circuits and cables all have an impedance of 50 Ω. It is for this reasen that splitters consisting of a delta connection of three 50 Ω resistors R. (refer to 1). In each part, the resistance is: (R + Z 0 ) (R + Z 0 ) = 50 Ω 3 The experiment 3.1 Spectrum analyzer Measuring the frequency Using the function generator, generate a sine wave with a frequency of 20 MHz and examine that signal with the spectrum analyzer! Set center frequency equal to 20 MHz and span to 50 MHz or 100 MHz! Hint: To check for correct setting of function generator, connect an oscilloscope. Also in the negative frequency range of the spectrum analyzer you will see some signal, wich merely are mirrored at zero frequency axis. 2

Abbildung 1: symmetric splitter 3.1.2 Analyzing the spectrum Generate a rectangular (square) wave. Observe the spectrum and explain, taking into account Fourier transform, width and shape! 3.1.3 Electromagnetic shielding, antenna Connect an unshielded able to the input of the spectrum analyzer.

3 Abbildung 1: symmetric splitter Analyzing the spectrum Generate a rectangular (square) wave. Observe the spectrum and explain, taking into account Fourier transform, width and shape! Electromagnetic shielding, antenna Connect an unshielded able to the input of the spectrum analyzer. This cable will act as an antenna. Find some distinct signals and assign them to nearby radio stations. You can use the following table as a guide 1: station NDR1 Antenne MV Ostseewelle frequency 95,8 MHz 97,3 MHz 105,6 MHz Tabelle 1: Some selected public radio stations in Rostock and their frequencies Now, replace the unshielded cable by a coax cable and describe what happens Using the spectral analyzer as a receiver Adjust the center frequency such that it coincides with one of the radio frequencies with high signal strength. Apply the following settings: VBW (video bandwidth) 4 khz (noise reduction) RBW (resolution bandwidth) 120 khz (sampling extends the range of human oral perception) Attenuation -10 db bandwidth 0 MHz (zero span) (thus, temporal evolution of amplitude at center frequency is displayed) Connect head phones and adjust volume. Now change center frequency by some khz! Compare the modulation of the signal at the edges with modulation at center frequency. Beside ultra short wabe band (USW), further frequency bands can be received. Assign some of them to technical applications, such as the range around 900 MHz (e. g. D net uplink MHz, downlink MHz)! 3

4 USW radio stations transmit with frequncy modulation (FM), while long, medium and short wave radio stations use amplitude modulation (AM). Conclusion: Use only shielded coax cables for the following experiments! 3.2 time domain measurements Use the function generator to generate pulses with a duration of less than 20 ns! Split this signal using a splitter. One part is sent to a long cable with an open end. The other part part and the back-travelling signal from the stub is displayed on the oscilloscope. (refer to 2). Abbildung 2: Setup to investigate reflexion at the open end Reflexion The open stub shall be closed with different impedances. In doing so, discuss the following cases: Z < Z 0, in particular closed end Z Z 0 Z > Z 0, in particular open end How is the situation changed, when a simple BNC T-piece adapter is used instead of the symmetric splitter? Also, repeat the measurement, after having extended the stub using either symmetric or unsymmetric splitter? In this context, explain time domain reflectometry! wave velocity Determine the velocity of the electromagnetic wave using the measurements done in temporal domain. Describe the differences between phase velocity, group velocity, and signal velocity. Explain the results of your measurements dispersion Determine the width of the initial signal and compare it to the duration of the reflected signals. How strong is the broadening, and how can it be explained? 3.3 frequency-dependent signal transmission Use the tracking generator as the source. 4

3.3.1 Damping Connect the tracking generator to the spectrum analyzer directly using a very short BNC cable. Repeat, but this time with a very long cable. What can be observed?

The other part part and the back-travelling signal from the stub is displayed on spectrum analyzer. (refer to Fig. 3) What can be observed?

5 3.3.1 Damping Connect the tracking generator to the spectrum analyzer directly using a very short BNC cable. Repeat, but this time with a very long cable. What can be observed? Add an attenuator to the connection. Again, what can be observed? velocity of propagation Split the signal using the splitter: One part is sent to a cable with an open end. The other part part and the back-travelling signal from the stub is displayed on spectrum analyzer. (refer to Fig. 3) What can be observed? Find out in which manner the position of the maxima depends on the length of the open-ended cable! Abbildung 3: Reflection of the split signal at the open-ended cable. Abbildung 4: Reflection at a terminated or partially terminated cable using a variable resistor. In the cable with open termination, the wave is reflected back at the end. Forth-propagating and backward reflected wave superpose to form a standing wave. Calculate the velocity of propagation of the electromagnetic wave in the cable. Berechnen Sie die Ausbreitungsgeschwindigkeit von elektromagnetischen Wellen im Koaxialkabel. Use the values obtained in the spectral domain for that calculation Reflection The end of the coax cable shall now be connected with different terminators, see Fig.4. Discuss the three cases: Z < Z 0, in particular short circuit termination Z Z 0 Z > Z 0, in particular open termination How is the stub in this experiment related to the sound generation in a flute? Decide in which case you have a vibration node (zero elongation at that point) and an antinode (elongation unequal zero) at the end of the cable! It may be helpful to take an additional measurement in the time domain into account. 5

3.4 multi-path filter 3.4.1 two-path filter Set up the two-path filter as shown in Fig.. 5! Use the pulse generator as a source.

6 3.4 multi-path filter two-path filter Set up the two-path filter as shown in Fig.. 5! Use the pulse generator as a source. The delay line should have a length of 5 m, and all other cables should be very short. Use symmetric 50 Ω splitters to avoid reflections! The signal is sent through the filter, and the output is examined with the oscilloscope. Explain the result. Calculate the pulse delay τ between the two pulses based on the length difference of the two signal ways! Now, display the output on the spectrum analyzer! The visible spectrum is an interference between the individual pulses. When pulse duration is changed, how does that influence the spectrum, in particular the separation of the minima and maxima? Abbildung 5: Setup to investigate the two-path filter path filter Increase the filter to five paths, as shown in Fig. 6! Investigate the transmitted signal both in the time domain and spectal domain! Explain the filtering-effect of the circuit. What influence do the variable attenunations and the variable delay lines have? Simulation of multi-path filters Use a computer algebra system (Mathematica) to simulate the two-path filter. For that purpose, source code is provided. Explain the different steps in the code. Simulate the five-path filter. What influnce do the repetition frequency, the phase shift and the length of the window used for Fourier transform have on the output signal? 4 Annotations It may be surprising that a lossless cable a combination of capacitors and inductors is described by a purely real resistance, which, however, can not be measured with a conventional resistance meter. Still, the understanding of this concept is of great importance not only in high-frequency technology, but also for example in optics and acoustics. The concept of the wave resistance corresponds to, for example, the 6

$Abbildung 6: Setup to investigate the five-path filter. refractive index in optics.$

7 Abbildung 6: Setup to investigate the five-path filter. refractive index in optics. An impedance matching corresponds to the matching of refractive indices and allows a transmission of a wave without reflection. In this context, answer the following questions! Under which conditions will a source, having a certain internal resistance, transfer maximal power to a load resistance? I a swimming pool, why can you barely hear the voices of other bathers when you dive? If there is a splinter of glass a bottle with cooking oil, it s invisible. Why? How is the two-path filter related to the Mach-Zehnder interferometere in optics? What is the relation between reflections in coax cables and Newton s rings in optics? How does the experiment in section 3.3 relate to the Gires-Tournois interferometer in optics? The Fourier transform, that relates frequency and time domain, is of central importance in many areas in physics. Here, you realized a filter (acting on the spectrum) by delay lines and interference (working in time domain). 4.1 material list spectrum analyser with tracking generator: Hameg HM oszilloscope: Hameg HM 2005 function generator (pulse width < 20 ns) 10 impedance matched splitters attenuators (2 times 3 db, 2 times 10 db) 10 short coax cables (< 1 m) 7

8 5 coax cables 1 m to 5 m 1 coax cable 10 m 1 unshielded cable (antenna) 4 terminators (resistance 50 Ω) 1 variable terminator (resistance Ω) 1 tape measure (3 m) Literatur [1] Bedienungsanleitung Oszilloskop Hameg HM 2005 [2] D GB.pdf Bedienungsanleitung Spektrum-Analysator Hameg HM [3] R. W. Hamming, Digitale Filter, VCH, 1997 [4] R. Unbehauen, Systemtheorie 1; Allgemeine Grundlagen, Signale und lineare Systeme im Zeit und Frequenzbereich, Oldenburg. [5] Ohm, Lüke, Signalübertragung, Springer [6] M. Werner, Signale und Systeme, Vieweg Betreuer Philipp Rohrmann: Universitätsplatz 3, Zimmer 118, Tel. 6823, philipp.rohrmann (at) unirostock.de 8

TileCal Analogue Cable Measurement Report

TileCal Analogue Cable Measurement Report Weiming Qian w.qian@rl.ac.uk +44-1235-446128 Rutherford Appleton Laboratory, UK 25 August 2005 Contents Contents... 2 1 Scope... 3 2 Impedance measurements... 3 2.1 Test setup... 3 2.2 Differential mode