PERIOD DOUBLING ROUTE TO CHAOS FOR A 1GHZ NONLINEAR MICROWAVE PHASE LOCKED LOOP USING MICROSTRIPPED GAUSSIAN PASS-BAND FILTER A. FISCHER(1), M. CHENAVAS(2), S. BENSMIDA(3). Laboratoire de physique des lasers , UMR 7538, université de Paris 13, Laboratoire de mathématique d'Analyse et de Géométrie appliquée, Université de Paris 13, Laboratoire de radiocom, Ecole nationale supérieur des télécoms, Paris, France,

Abstract : We report a period doubling route to chaos in a 1GHz VCO set up in a phase locked loop scheme. The system includes a 600-1200Mhz voltage controlled oscillator, a microstrip-based Gaussian-type pass-band filter centred at 900MHz, a microstrip designed

envelop-detector, and amplifiers, in a 10µs delayed feedback loop. Under

certain conditions on the feedback gain the system exhibits 20µS based periodics oscillations. We show that the gain of the feedback loop control the 20µS based regular oscillations and lead them to chaos through a period doubling route to chaos. A Potential application deals with encrypted radio communications and or chaotic-coded division multiplexing access.

Keyword : Chaos, microwave, microstrip pass-band filter, period doubling route to chaos, voltage controlled oscillator.

Introduction :

Description of the setup :

The system shown in figure 1 consists of a voltage controlled oscillator, a pass band filter, an amplifier, an envelop detector followed by a double stage amplifier, a 10µs delay. The feedback loop is closed through a coupler. The voltage controlled oscillatorVCO is a Minicircuit ZOS-1025, with a 600-1200MHz tuning range and a 100KHz 3dB-modulation bandwidth, and a 8dBm output power and a 12V supply voltage. It's frequency output f as a function of the DC input voltage V is shown fig. 2 and appear to be linear in a good approximation :

f(v) = f0 +ν.V

Eq.1

Where f 0 = is the frequency output for V=0 and ν=30?? MHz is the sensitivity of the VCO. The VCO is followed by a microstrip-designed gaussian type pass-band filter (fig 3a) centred on 912MHz with a 50MHz half width at half maximum (HWHM), which transfer curve is shown fig. 3b. Its normalised maximum transmission is 0,457 which corresponds to a –3,4dB attenuation. The transmitted voltage Vfilter at the ouput of the filter as a function of the input frequency is then :

V filter(f)=0,457 gaussian (f − f0) ??

Eq. 2

after the filter the wave is amplified through a ZFL-1000 Minicircuits amplifier with a 8dBm maximum ouput power and a 5dBm no damage input. The average gain is G1=17dB, but a change of the supply voltage in between 10V and 18V produces a gain change in the 15dB19dB range allowing more than doubling the amplitude of the microwave. The microwave is then injected in a 50/50 power splitter (ZFSC-???? Minicircuits). Part of the wave goes to the diagnostic part of the setup which will be describe further below. Half of the microwave is transmitted through a –3DB attenuator to the envelop detector. The latter consists of a 50Ω micro strip with a 5??pF serial capacitor, a 5kΩ resistor and ended with a high speed rectifier diode (HMS-2850), and a microstripped 900MHz absorber???. The output of this envelop detector is a low frequency signal and is followed by the first stage of the amplifiers. It consists of an operational amplifier with a 5V supply voltage, a 900MHz gain-bandwidthproduct and a gain set to G2=5???(OPA 658). A second stage of amplification includes a 15V supply voltage operational amplifier THS???? with a gain equal to G3=10??. The resulting cutting frequency of both amplification stages is 20MHz. A 1600m long BNC cable is then used to obtain a T=8µS delay with a neglectable attenuation for low frequency signal (