Design Ideas: March 31, 1994

At the heart of many oscillators is a parallel-resonant LC tank circuit whose impedance is infinite at the resonant frequency of 1/2[pi]ÖLC Hz. Infinite impedance implies an absence of parallel damping resistance, so once an ideal tank circuit starts oscillating, it should continue indefinitely. An actual tank circuit, of course, has parasitic resistances that dissipate energy, causing the oscillations to die out. You can counteract this effect by adding a "negative" resistance, which cancels the net parallel parasitic resistance. Fig 1a's circuit uses a wideband transconductance amplifier to synthesize negative resistance easily.

This circuit connects the positive input of the amplifier, a MAX436, to its output and its negative input to ground. With this configuration, applying a positive voltage to the output causes current to flow out of the amplifier in proportion to the applied voltage. The circuit acts like a resistor whose current flows in the opposite direction; hence, the negative value. Note the equivalent circuit in Fig 1b.

The source impedance of the amplifier's current-source output, a minimum of 2.5 k Ohm, is compatible with load resistances that range from 50 to 300 Ohm. The load resistance in this circuit, R₂, is 47 Ohm and should be much smaller than the tank-circuit parasitics, yet larger in absolute value than the amplifier's negative resistance. R₁ sets the negative resistance in terms of the amplifiers' transconductance, g_m=8/R₁, where factor 8 is inherent in the amplifier.

The negative resistance value is, therefore, equal to the value of R₁/8, which must be less than R₂. Choosing 47 Ohm for R₂ yields R₁<8*r₂=376 Ohm. A reasonable value for R₁, therefore, is 301 Ohm. As intended, the parallel combination of negative resistance, which is -R1/8 or -37.6V, and a positive R₂ of 47 Ohm yields a negative resistance of -189 Ohm that shifts the oscillator's complex-conjugate pole pair to the right half plane.

By itself, the combination of tank circuit and regenerative element-the negative resistance-simply drives the output amplitude to saturation. To achieve steady oscillation, the circuit needs an amplitude limiter. R₃ serves that purpose and appears, in parallel with R₂, only when the amplitude is sufficient to turn on D₁ or D₂.

Then, excluding the diode resistance, the net parallel resistance is a positive value of 63 Ohm-two parallel 47 Ohm resistors in parallel with -37.6-that damps oscillation by shifting the pole pair to the left half plane. Thus, the circuit achieves amplitude stability by allowing the pole pair to toggle between positions slightly to either side of the jv axis.

The oscillator, whose tank circuit consists of a mica capacitor and an air-core inductor, has an output frequency of 9.3 MHz. You can trim the output frequency to any reasonable value, but above 10 MHz, the layout should include short connections and a ground plane. The output power spectrum for Fig 1 indicates that the major source of THD is a third harmonic below -40 dB, which is less than 1%. After you apply power, the oscillator requires approximately 350 µsec to reach its final amplitude. EDN BBS/DI_SIG #1392