BACKGROUND

In U.S. Pat. No. 8,072,281 (“Hanafi”), entitled “Method, system and apparatus for accurate and stable LC-based reference oscillators,” issued Dec. 6, 2011 and incorporated herein by reference, the Temperature Null (TNULL) phenomenon has been analyzed and illustrated. On operating an LC tank at its TNULL phase, the oscillation frequency exhibits minimal frequency variation versus temperature. Related U.S. Pat. No. 8,884,718 entitled “Method and apparatus to control the LC tank temperature null characteristic in a highly stable LC oscillator,” issued Nov. 11, 2014, is also incorporated hereby by reference.

The oscillator which can force the LC tank to oscillate at its TNULL phase utilizing the TNULL phenomenon is said to be a “TNULL oscillator”. It is also called a “Self-Compensated Oscillator” in the sense that it exhibits minimal frequency variations across temperature without the need for external compensation circuitry. It is denoted as “SCO” for simplicity.

FIG. 1presents the generic SCO. The oscillator consists of:1. An LC tank circuit101to define the oscillating frequency.2. A gm-cell103to compensate the losses of the tank circuit to start and sustain oscillations.3. A phase block (Φ)105to adjust the phase of the tank impedance.

Herein, the phase Φ is programmed such that it is as close as possible to the inverted tank TNULL phase “—ΦGNULL”; thus the phase of the tank impedance becomes ΦGNULL. This is achieved by equating the frequency at the temperature range extremes To−ΔT and To+ΔT. In this case, the frequency deviates within this temperature range by the oscillator inherent behavior and no mechanism is applied to control the oscillator behavior.

The profile of the frequency variation versus temperature at the TNULL phase is denoted by the “Temperature Null Characteristic” or the “TNULL Characteristic”.

In Hanafi, a first order model for the tank variation versus temperature was analyzed and the theoretical expectation for the TNULL characteristic was introduced as shown inFIG. 2. The first order model of the tank versus temperature included the temperature variations of the inductor DC (direct current) losses only.

Practically, there are other factors that affect the TNULL characteristic, such as and not limited to:1. The temperature varying harmonics induced by the active circuitry.2. The temperature varying parasitic capacitances imposed by the routing interconnects and the active circuitry.3. The temperature varying non-ideal effects in the inductor of the tank such as the skin depth effect and the proximity effect.4. The temperature variation of the capacitance of the tank.

Due to such factors, the practical TNULL characteristic deviates from the theoretical expectations of the first order model. The shape of the practical TNULL characteristic varies according to the weight of each factor and the combination of the different factors.FIG. 3compares three examples for possible practical TNULL characteristics to the theoretical TNULL characteristic as expected based on the first order model. The TNULL characteristic is the shape of the frequency deviation Δf(T) versus temperature, where Δf(T) is the frequency deviation referred to the oscillation frequency at the extremes of the temperature range To−ΔT and To+ΔT when operating at TNULL. Note that the frequency at the temperature range minimum To−ΔT is equal to the frequency at the temperature range maximum To+ΔT on operating at TNULL. This equality is an intrinsic feature of the TNULL characteristic since the TNULL phase is obtained by equating the phase-frequency plots at both To+ΔT and To−ΔT. Hence, Δf(T) is given as:

Δ⁢⁢f⁡(T)=f⁡(T)-f⁡(To-Δ⁢⁢T)f⁡(To-Δ⁢⁢T)=f⁡(T)-f⁡(To-Δ⁢⁢T)f⁡(To+Δ⁢⁢T)

The excursion in the TNULL characteristic from the nominal frequency in the temperature range of To−ΔT to To+ΔT has several disadvantages such as increasing the overall frequency deviation versus temperature, complicating the trimming and calibration process and violating the initial accuracy specification which is the value of the frequency deviation at Tothat is usually the room temperature.

SUMMARY

Techniques are described that enable controlling the TNULL characteristic by controlling the magnitude and direction of the frequency deviation versus temperature, and thus, compensating the frequency deviation.

It is worth noting that compensating an SCO operating at TNULL is more convenient than compensating a conventional LC oscillator operating at a phase away from ΦGNULL, for example as in U.S. Pat. Nos. 7,332,975 and 8,134,414. This stems from the fact that the magnitude of the frequency deviation of the SCO is much smaller than that of the conventional LC oscillators. Thus, the SCO offers a better initial point to apply frequency compensation which yields the following advantages in the compensation system:1. Operating at TNULL requires a smaller dynamic range for the compensation circuits because the frequency excursions that should be compensated in the case of the SCO are appreciably smaller than those in the case of the conventional LC oscillator.2. Lower frequency deviation at TNULL implies that a lower temperature-to-frequency gain is required at the compensation loop, resulting into lower noise translation from the temperature sensor and the compensation circuitry to the oscillator output phase noise.3. The oscillator may become less sensitive to process corners when trimmed to operate at TNULL.

