The design of low-phase-noise oscillators requires careful attention to resonator unloaded Q. In the construction of a low-phase-noise, high-frequency oscillator, the goal is to achieve an unloaded-Q figure greater than 400 in a reasonable package. Also, you need to monitor the effect of the package and pc-board arrangement. Shielding, inappropriate grounding, and some construction techniques can degrade unloaded Q. Q meters; various bridges, such as Maxwell and Hayes; and both vector and scalar impedance analyzers are useful but inconvenient-to-use test instruments. You must carefully set up test fixturing and calibration that duplicates the final environment to obtain reasonable agreement with the final measured results. A simple test set uses nothing more than the voltage-divider relation with the device under test embedded as a series trap network (Figure 1). You can measure the inductor's value, or calculate it from known equations based on the inductor's form factor, such as solenoid, toroid, helical, or flat spiral. You use the inductor's value to select C₁, a variable, air-dielectric high-Q capacitor. At resonance, the impedance of the inductor-capacitor combination goes to zero, so the effective load is the series resistance R_S in parallel with the 50Ω termination resistance.

You use an RF generator and voltmeter to read the depth of the notch the trap creates. This attenuation depth is a function of the remaining finite-series resistance of the resonator. Table 1 shows the notch attenuation for R_S ranging from 0.1 to 1Ω. These values assume 50Ω source and termination impedance and the component values shown in Figure 1. Unloaded Q equates to X_L/R_S, where X_L is the reactance of the inductor, and R_S is the equivalent series resistance. Figure 2 shows the notch attenuation as a function of the equivalent series resistance. In addition, a crosscheck is available: You can the 3-dB bandwidth of the notch and calculate unloaded Q from f₀ divided by the bandwidth. Finally, as a "sanity check," you can readily reduce the unloaded Q to a known value by inserting a series resistance in the trap circuit. The reduction in unloaded Q should correlate with added resistance value. Any variations you notice in these simple experiments are usually the result of subtle factors. One factor in particular is a component operating near its self-resonant frequency. In the test case of Figure 1, six-gauge wire on a 0.75-in. Delron rod with careful construction lets you achieve unloaded Q near 500 at 70 MHz. The measurement technique unveils issues with shielding, namely the reduction in Q from the effect of the shield on the solenoid coil. The details of the measurement are as follows:

Assume an inductor with known L and X_L at a frequency of interest f₀. The inductor shall resonate in a series-tuned (trap) configuration, driven from a 50Ω generator and terminated in a 50Ω shunt. An RF voltmeter placed across the shunt reads notch depth in decibels. From Figure 2, you can determine the unloaded Q from the expression Q=X_L/R_S. For example, a solenoid inductor measuring 0.75 in. in diameter and wound with five turns of six-gauge wire has a measured inductance of 460 nH at 65 MHz. The inductor series-resonates at 65 MHz with a 13-pF capacitor. You set the signal generator at 65 MHz and use a variable, air-dielectric capacitor to fine-tune the notch at 65 MHz. The measured notch depth is 36 dB. R_S is 0.4Ω, and the unloaded Q is 469. You can readily notice changes in the depth of the notch with fine variations in coil position relative to conducting surfaces.

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