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RF Electronics Chapter 6: Oscillators Page 186 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. oscillators. The phase noise of the Hartley common collector (CC) oscillator is within 1 dB to that of the Colpitts oscillator shown in figure 6.14. The common emitter (CE) Hartley oscillators have a similar phase noise, and their phase noise is 10 dB worse than that of the common collector oscillator. To ensure that a fair comparison can be made between the performance of the oscillators in figures 6.10 and figures 6.17 to 6.19, the same transistor and the same resonator total inductance and capacitance values are used. Normally the Q of the capacitors used in the resonator is much higher than the Q of the inductors, so that the Q of the resonator is determined by the Q of the inductor. A Q of 200 can be achieved by careful construction of the inductor used for the resonator. The designs presented above are for a 100 MHz oscillator. The resonator elements are calculated using equations in AWR DE, so that the oscillation frequency can simply be changed by changing one variable. Since the amplitude of the waveform across the OSCAPROBE element may be larger than the secondary parameter VpMax, that value should be increased to 8V. It is also important to set the value of FC in the OSCTEST element to 160MHz, which is greater than the frequency sweep used for the linear gain test and less than the expected 200 MHz second harmonic of the oscillating frequency. Practical Inductors Making the resonator impedance (Zrc) small will reduce the phase noise. However, that may result in unrealistic component values. Wheeler's [5] empirical formula for the inductance of a single layer air core is given as: � � � � � � ������ �r, l in inch and L in �H� Eqn. 6.1 The inductance; L is in H, the radius r and coil length l, are in inches and N is number of turns on the coil. Using the coil diameter d, and converting this to metric units gives the approximate metric version, which has the inductance in nH as: � � � � � � ��.������ �d, l in mm and L in nH� Eqn. 6.2 For RF coils, the highest Q is obtained when the spacing between the turns is about the same as the wire diameter. A closer spacing increases the capacitance between the turns and lowers the self-resonance of the inductor. A larger spacing reduces the inductance. Often the insulation covering the wire provides close to the required spacing for the optimum Q. AWG 26 gauge solid wire has a 0.405mm diameter, covered with 0.3�mm insulation, giving a total diameter of 1.165 mm. A d � 2.641 mm coil diameter, 3 turns will result in a coil length of 2x1.165 � 0.405 � 2.�35 mm and from equation 6.2, that coil will have an inductance of 16.00 nH, That is a reactive impedance of 10.053 ٠at 100 MHz. AWR DE implement more advanced calculations of this using the element COIL. Those equations, instead of the diameter to the centre of the conductor coil, require the inner coil radius, the radius of a former if the coil has no insulation. The above 2.641 mm coil diameter corresponds to a �2.641 0.405��2 � 1.11� mm inner radius. That results in a reactive impedance of 9.946 10 ٠at 100 MHz. Wheeler's formula and the AWR DE Coil element agree closely. The coil dimensions are about as small as one may wish to use for this design. As a result, we limit the impedance of the inductor's Zr to be 10 ٠or greater in this example. The inductance can be changed slightly by stretching or compressing the length of the coil. Figure 6.23 shows the Real and Imaginary part of RF Electronics: Design and Simulation 186 www.cadence.com/go/awr

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