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.

Choose the right quartz crystal for your energy saving MCU with THIS simple test

Next generation MCUs and RF chipsets, commonly used in IoT, wearable, and battery powered applications, have presented a problem frequently ignored by many designers across all industries. Lower power consumption requires next generation crystals to optimize for a weaker gain and drive from the Pierce analyzer. The ability to sustain oscillation for a given quartz crystal oscillator design depends heavily on the crystal’s motional parameters, board parasitics, and oscillator circuit characteristics. Yet, as MCUs are upgraded to lower power models, their crystal counterparts have stayed the same. The Pierce oscillator circuit, a closed loop system most commonly integrated into low power ICs, sustains oscillation at an operating point, depending on the crystal plating capacitance (CL), crystal equivalent series resistance (ESR), and oscillator amplifier’s gain and phase response associated with the oscillator’s transconductance (gm). But, how do you know if your crystal’s parameters match your system?

Abracon’s Pierce analyzer system (PAS) was designed by our engineers to help you make the right choice for your industry leading designs. The PAS test validates quartz crystal performance in-circuit and simultaneously measures the crystal, crystal oscillator, and printed circuit board parasitics. Testing in-system accounts for all variables and enables ideal matching of crystal parameters to the board and oscillator in the MCU or RF chipset. This is especially critical for applications using next generation, energy saving technologies requiring optimal gm factors.

Lower CL and lower ESR increase operating gain margin of the loop, ensuring sustained oscillations across all variables including variation in bias, loading, temperature, and over time. Gm_critical is the critical transconductance value that a crystal must achieve in order to remain in the safe zone of loop operation. Crystals that do not meet gm_critical are not well matched to the Pierce oscillator and may cause long term reliability issues associated with startup. Since lower power consumption decreases gm and gm_crictical for a given Pierce oscillator, energy saving designs deployed in IoT and wearables applications are the most at risk of failure. Conducting a PAS test reduces risk and improves the reliability of your system.

“Semiconductor technology strives to wring all the power consumption out of the latest generation of MCUs and RF chipsets,” commented Syed Raza, VP of Engineering with Abracon “the on-chip Pierce oscillator is starved of much needed gain negatively impacting the gm_critical metric. The PAS test is the surest way to diagnose preventable problems.”

“As The Heartbeat of the IoT™, we strive to provide customers with as many tools and services as possible that will take their designs to the next low power plateau. The PAS test service enables validation of a critical subsystem in the design given that nothing will operate if the oscillator fails to run.” commented Juan Conchas, Director of Marketing with Abracon.

The service provides a comprehensive report outlining the functional parameters of the oscillator circuit and recommends changes when necessary. This service is conducted by Abracon and can be ordered through any franchised distributor, with multiple turn-around times from 2-weeks to 4-weeks.

Learn more about the Pierce Oscillator here.
Find more information on the PAS test, here.

Check inventory for the PAS here: PAS-BC1WK/ PAS-BC2WK/ PAS-BC3WK

About Abracon, LLC
Founded in 1992, and headquartered in Spicewood, Texas, Abracon is a leading global manufacturer of passive and electromechanical timing, synchronization, power, connectivity and RF solutions. Abracon offers a wide selection of quartz timing crystals and oscillators, MEMS oscillators, real time clocks (RTC), Bluetooth modules, ceramic resonators, SAW filters and resonators, power and RF inductors, transformers, circuit protection components and RF antennas and wireless charging coils. The company is ISO9001-2008 certified with design & application engineering resources in Texas and sales offices in Texas, California, China, Taiwan, Singapore, Scotland, Israel, Hungary, UK, and Germany. Abracon’s products are offered through its global distribution network. For more information about Abracon, visit www.abracon.com.