Over Temperature Effects of Gm_critical | A Technical Review

The emergence of the IoT has accelerated the trend towards lower power consumption on many MCU and RF chipsets, pressuring IC designers to wring out every bit of energy savings in their circuits. The consequence, pertaining to the clocking scheme, is usually a weaker oscillator loop amplifier starved of transconductance (gm). The reduced power consumption has the potential to severely affect analog circuits, such as the Pierce oscillator.

The Pierce oscillator driving quartz crystals is one of the most common circuits in the electronics industry. Present in almost every microcontroller, RF chipsets, and many other IC’s, this circuit is the true workhorse of timing in almost every device developed today. As most design engineers employ negative resistance analysis to assess closed-loop dynamics, some may ignore another very significant metric – gm_critical.

As the name implies, gm_critical can be defined as the level of critical value of closed-loop transconductance mandatory to keep the amplifier in linear region, while maintaining sufficient forward gain at the desired phase shift of (n*2π). The closed-loop overall gain margin (GM) is mathematically represented as:

GM = gm / gm_critical ………. (1)

Whereas; gm = oscillator loop amplifier’s intrinsic transconductance (µA/V, or mA/V)
gm_critical = closed-loop transconductance needed to keep the amplifier in linear region with sufficient forward gain at the desired phase shift (µA/V, or mA/V)

It is a well-established industry figure of merit to target GM > 5, with minimum value of 3. With the reduction in the intrinsic gm value, it is paramount to simultaneously reduce the gm_critical needed for sustained oscillations.

It should be noted that gm_critical has significant dependence on the external resonator’s electrical characteristics at the desired resonant frequency and is outlined in equation (2).

gm_critical = 4 * ESR * (2πF)2 * (C0 + CL)2 ………… (2)

From equation (2) it is evident that any significant reduction in gm must be counter-balanced with a reduction in gm_critical to ensure that the closed-loop overall margin (GM) remains the same. For instance, consider the following example:

gm = 2.7 µA/V; GM = 5; then gm_critical = 0.54 µA/V maximum
Now, if the gm is reduced to 1.0 µA/V, to keep GM = 5; the gm_critical = 0.20 µA/V maximum

In equation (2) the three critical parameters that determine the feasibility of this counter-balance are the ESR, C0 and CL of the Quartz Crystal. To achieve lower gm_critical, all three of these parameters must be simultaneously reduced to ensure proper overall gain margin (GM), while the oscillator amplifier’s transconductance gm is lowered.

As the power optimized silicon expands its domination of the electronic industry, reducing the intrinsic gm, the gm_critical metric is the most important criteria to ensure robust oscillator loop performance.

Abracon’s family of newly released Performance Optimized IoT Crystals have been engineered to specifically address the falling transconductance values across the industry and are compatible with industry’s lowest gm_critical designs. The ABM8W/ABM10W/ABM11W/ABM12W MHz series are guaranteed to operate with gm_critical as low as 3.55mA/V for 50MHz operation. The ABS06W/ABS07W 32.768kHz Tuning Fork Crystals are guaranteed to operate with industry lowest gm_critical value of 0.276µA/V @ 25°C in 2.0×1.2×0.6mm and 0.191µA/V @ 25°C in 3.2×1.5×0.9mm packages.

Plots A and B represent over extended temperature oscillation sustainability matrix of these state-of-the art 32.768kHz solutions ideally suited for energy saving RTC applications.

As transconductance (gm) of most Pierce oscillators dive to unprecedented low levels, quartz crystals have to adapt to maintain sustainable oscillations. Abracon has embraced and overcome this challenge by designing and producing, lower plating load capacitance (CL) and lower equivalent series resistance (ESR) Crystals, while simultaneously lowering the (electrode package) capacitance C0.

Meeting the lowest gm_critical requirements demanded by energy saving MCUs and RF chipsets means guaranteed low CL, ESR and C0. Abracon’s specialized design and processing techniques address this paradigm shift and brings both MHz and kHz Performance Optimized Quartz Crystals to the market. Uniquely engineered for the IoT/Wearable/Consumer Electronics market, these crystals are ready for the future of lower power engineering.

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