A CRYSTAL-LESS CLOCK THAT IS INVARIANT WITH PROCESS, SUPPLY VOLTAGE, AND TEMPERATURE

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the benefit of U.S. Provisional Patent

Application No. 62/379,206, filed on August 24, 2016, entitled "A CRYSTAL-LESS CLOCK THAT IS INVARIANT WITH PROCESS, SUPPLY VOLTAGE, AND TEMPERATURE," U.S. Provisional Patent Application No. 62/370,602, filed on August 3, 2016, entitled "A CRYSTAL-LESS CLOCK THAT IS INVARIANT WITH PROCESS, SUPPLY VOLTAGE, AND TEMPERATURE," and U.S. Provisional Patent Application No. 62/302,734, filed on March 2, 2016, entitled "TEMPERATURE AND SUPPLY INDEPENDENT RC OSCILLATOR," the disclosures of which are expressly incorporated by reference herein in their entireties.

BACKGROUND

Technical Field

[0002] The present disclosure relates generally to oscillator circuits, and in particular to crystal-less clock circuits that are independent of process, supply voltage, and temperature.

Background

[0003] Crystal-less clock sources are desirable in many applications. While a crystal oscillator (XO) may have superior period jitter, it suffers from two limitations. First, the startup time of the XO is typically on the order of milliseconds. Secondly, the amount of electric current to operate a crystal oscillator is typically on the order of milliamps. For example, a commercial 19.2MHz XO may take up to 50ms to start up while drawing 2.5mA of current from a 3 V supply.

[0004] Conventional crystal-less oscillator designs have various shortcomings. Ring oscillators, for example, generally have inherently high variation over both power supply voltage (V) and temperature (T). Compensating a ring oscillator for voltage and temperature (VT) variations can be difficult. LC -based oscillators can offer inherently high VT independence; however LC oscillators tend to be area intensive and not suited for low frequency applications. [0005] An RC relaxation oscillator has a frequency that is primarily set by the RC product, so it has a naturally high V independence. Further, by realizing capacitor C using MOMCAP technology (which have a temperature coefficient of zero), the remaining source of variation is the temperature dependence of the resistor R. In traditional CMOS RC oscillators, this issue can be addressed in some technologies by building the resistor as a weighted sum of two materials having opposing temperature coefficients; for example, by combining poly and diffusion resistors in a suitable ratio. However, this passive approach has its limitations. Building two such resistive materials may involve additional implants or special processing steps, thereby increasing fabrication costs. Moreover, in some technologies (e.g., Fin Field Effect Transistors (FinFETs)) this approach is not even an option, as only one kind of high resistivity material that is production-worthy is available. Even in technologies that offer two resistors with opposing tempcos, if one (or both) resistors shows large enough process variations, this method does not work well and can result in large variation of the combined tempco.

SUMMARY

[0006] In an aspect of the present disclosure, a method of generating a bandgap voltage in an electronic circuit is presented. The method includes generating a bandgap current. The method further includes operating the electronic circuit using the bandgap voltage and the bandgap current. The operating may be based on a ratio of the bandgap voltage to the bandgap current.

[0007] In another aspect of the present disclosure, a circuit is presented. The circuit has a first current generator configured to generate a first current that varies with temperature, as well as a second current generator configured to generate a second current that varies with temperature in opposite relation to the first current. The circuit further includes a voltage generator, connected to the first and second current generators, which has an output for a bandgap voltage based on the first current and the second current. The circuit further includes a current generating circuit connected to the first current generator and the second current generator that has an output for a bandgap current based on the first current and the second current. The circuit also includes a capacitor selectively configurable in a first configuration to receive the bandgap current to charge the capacitor and a second configuration to discharge the capacitor. The circuit further includes a comparator configured to produce a comparator signal based on the reference voltage and a capacitor voltage across the capacitor. The capacitor is configured in the first configuration and the second configuration in response to the comparator signal. The comparator signal varies in time in response to the capacitor being charged and discharged. The comparator signal has a period that is based on the reference voltage across a resistor and the charging current.

[0008] In yet another aspect of the present disclosure, a circuit is presented. The circuit includes an RC oscillator having a proportional to absolute temperature (PTAT) core and a complementary to absolute temperature (CTAT) core configured to generate a bandgap voltage and a bandgap current. The RC oscillator is configured to generate a temperature invariant oscillatory signal having a period that is based on the voltage and the current. The circuit further includes a frequency generator and a calibration engine. The calibration engine has an output for a multiplier and is configured to produce the multiplier based on the temperature invariant reference frequency of the RC oscillator and an external reference frequency. The frequency generator is configured to generate an output signal by regulating a frequency of the output signal to the temperature invariant reference frequency of the RC oscillator times the multiplier to produce a temperature invariant output frequency.

[0009] In still another aspect of the present disclosure, a circuit includes a first current generator configured to generate a first voltage that varies with temperature. The circuit also has a second voltage generator configured to generate a second voltage that varies with temperature in opposite relation to the first voltage. The circuit further includes a current generating circuit, connected to the first and second current generators, that has an output for a bandgap current based on the first voltage and the second voltage. The circuit also includes a voltage generating circuit connected to the first voltage generator and the second voltage generator that has an output for a bandgap voltage based on the first voltage and the second voltage. The circuit further includes a capacitor selectively configurable in a first configuration to receive the bandgap current to charge the capacitor and a second configuration to discharge the capacitor. The circuit further includes a comparator configured to produce a comparator signal based on the bandgap voltage and a capacitor voltage across the capacitor. The capacitor is configured in the first configuration and the second configuration in response to the comparator signal. The comparator signal varies in time in response to the capacitor being charged and discharged. The comparator signal has a period that is proportional to a ratio of the reference voltage across a resistor and the charging reference current.

[0010] Additional features and advantages of the disclosure will be described below. It should be appreciated by those skilled in the art that this disclosure may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the teachings of the disclosure as set forth in the appended claims. The novel features, which are believed to be characteristic of the disclosure, both as to its organization and method of operation, together with further objects and advantages, will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] With respect to the discussion to follow and in particular to the drawings, it is stressed that the particulars shown represent examples for purposes of illustrative discussion, and are presented in the cause of providing a description of principles and conceptual aspects of the present disclosure. In this regard, no attempt is made to show implementation details beyond what is needed for a fundamental understanding of the present disclosure. The discussion to follow, in conjunction with the drawings, makes apparent to those of skill in the art how embodiments in accordance with the present disclosure may be practiced. Similar or same reference numbers may be used to identify or otherwise refer to similar or same elements in the various drawings and supporting descriptions. In the accompanying drawings:

[0012] FIGURE 1 shows a clock source in accordance with some aspects of the present disclosure.

[0013] FIGURE 1 A shows details of calibration engine in accordance with some aspects of the present disclosure.

[0014] FIGURE IB illustrates an example of a frequency generator that can be adapted for in a clock source in accordance with the present disclosure. [0015] FIGURE 2 is a high level block diagram of a temperature independent circuit for realizing a temperature independent resistance quantity in accordance with the present disclosure.

[0016] FIGURE 2A shows a high level block diagram of the temperature invariant oscillator (TIO) of FIGURE 1 in accordance with the present disclosure.

[0017] FIGURE 3 shows some details of an exemplary temperature independent oscillator in accordance with the present disclosure.

[0018] FIGURES 3 A and 3B illustrate different operational states of the temperature independent oscillator shown in FIGURE 3.

[0019] FIGURE 3C shows some illustrative timing charts in accordance with the present disclosure.

[0020] FIGURE 4 illustrates an exemplary bias for a temperature independent oscillator in accordance with some aspects of the present disclosure.

[0021] FIGURE 4A illustrates an exemplary bias for a temperature independent oscillator in accordance with aspects of the present disclosure.

[0022] FIGURE 4B illustrates an exemplary bias for a temperature independent oscillator in accordance with aspects of the present disclosure.

[0023] FIGURE 5 illustrates examples of voltage-temperature behavior of p-n junctions.

DETAILED DESCRIPTION

[0024] In the following description, for purposes of explanation, numerous examples and specific details are set forth in order to provide a thorough understanding of the present disclosure. It will be evident, however, to one skilled in the art that the present disclosure as expressed in the claims may include some or all of the features in these examples, alone or in combination with other features described below, and may further include modifications and equivalents of the features and concepts described herein.

[0025] In accordance with the present disclosure, a high performance, high precision clock source can be realized without an externally supplied crystal reference (crystal- less). Referring to FIGURE 1, for example, a clock source may be realized as a crystal - less oscillator circuit ("oscillator") 100. In accordance with the present disclosure, the oscillator 100 may include a temperature invariant (insensitive, independent, etc.) oscillator (TIO) 102 to serve as a reference generator, and a frequency generator 104. The TIO 102 may produce a signal at an output 112. The frequency generator 104 may produce an output signal 114 using the signal at output 112 as a reference frequency

[0026] In some aspects, the reference frequency /REF may be bounded, but otherwise unpredictable; for example, /REF may vary plus or minus some percentage about a mean value. Merely to illustrate this point, suppose the TIO 102 is designed for 19.2 MHz operation. The actual operating frequency may vary (e.g., ± 20%) from one instance of the TIO 102 to another. This can arise, for example, due to tolerances in the devices used make the TIO 102. For example, process variations can result in devices having slight variations in operating characteristics. The resulting variations in the fabricated devices can affect the actual value of the reference frequency / _RE F and hence the output frequency four-

[0027] In accordance with aspects of the present disclosure, the oscillator 100 may include a calibration engine 106. The calibration engine 106 may be used to perform a digital frequency locked loop calibration based on the actual value of a given reference frequency /REF- The calibration engine 106 may generate a multiplier 116 that can be provided to the frequency generator 104. The frequency generator 104 may generate an output signal 114 having a frequency /οκτ that is a product of the reference frequency /REF and the multiplier 116. In some aspects, the multiplier 116 may be an integer valued multiplier. In other aspects, the multiplier 116 may include a fractional part and the frequency generator 104 may be a frequency synthesizer that operates in fractional mode and multiplies the reference frequency /REF with the fractional multiplier 116.

[0028] The calibration engine 106 may include a signal input for the reference frequency / _RE F and a signal input for an external reference frequency / _X REF- The external reference frequency f _xRE F may be a very stable, very accurate frequency source. In some aspects, for example, the external reference frequency / _X REF may be provided from a crystal oscillator. A switch 12 may be provided to switch in or switch out the external reference frequency / _X REF- For example, during manufacturing a crystal oscillator having frequency f _xRE F may be connected to the calibration engine 106 (e.g., switch 12 is CLOSED) for calibration purposes, and subsequently disconnected when calibration is complete (e.g., switch 12 is OPEN). In some aspects, the calibration engine 106 may include an n-bit data input 108 for a scale factor. This scale factor may be a pure integer or a decimal value (e.g., the scale factor can also include a fractional part).

[0029] Referring for a moment to FIGURE 1 A, in some aspects the calibration engine 106 may include a divider module 106a configured to receive the_/ and mF signals fxref

and produce a value that represents the ratio . In some aspects, for example, the

divider module 106a may comprise lo ic (e.g., field programmable gate arrays) configured to compute the ratio and mF, e.g., by

counting pulses (or edges) in the_7 and f _xRE F signals. The calibration engine 106 may fxref

include a multiplier module 106b configured to multiply the ratio with the n-bit

scale factor 108 to produce the multiplier 116, representing the quantity

fxref

x scale factor . In some aspects, the multiplier module 106b may comprise logic

(e.g., field programmable gate arrays) configured to compute the multiplier 116. In other aspects, the calibration engine 106 may comprise a processing component (e.g., central processing unit, digital signal processor, general IO processor, etc.) configured (e.g., with program code) to compute the multiplier 116, and so on.

[0030] Returning to FIGURE 1, the output frequency four of frequency generator 104 becomes f _ref x ^f x scale factor , which can be reduced to f _xref x scale factor

Notably, _7¾£ , which is an unpredictable quantity, falls out of the computation. Thus, a target frequency frARGET may be set by choosing an appropriate value for scale factor 108 for a given frequency f _xRE F of the external oscillator, independently off _RE F- While the external reference frequency f _xRE F (e.g., a crystal) may provide a stable reference, the scale factor 108 can provide the ability to specify frequencies for output signal 114. Because the scale factor 108 incorporates which is unpredictable with process but constant over temperature and supply voltage, mF can be omitted after a calibration output N.f (where N represents the integer portion, and f represents the fractional portion) is determined by the calibration engine 106. The output N.f (116) is determined by the calibration engine 106. N.f denotes a decimal value where N is the integer portion, and f is the fractional part. For example, if N.f is equal to 5.3, then N is equal to 5 and f is equal to 3. In some aspects, different frequencies for the output signal 114 may be generated during circuit operation by simply changing the scale factor value provided to the scale input 108.

[0031] Thus, although of a given TIO 102 may vary due to process variation, the multiplier 116 can be used to permanently correct for such deviations. To the extent that_7¾£ does not vary with temperature and supply voltage, the calibration can be a one-time procedure. For example, the calibration of TIO 102 using an external crystal oscillator to provide a stable frequency (/ _X REF) can be done during circuit test at the time of manufacture. After calibration, the external crystal oscillator is no longer used and can be switched out. The calibration can provide a precise output frequency four, and the TIO 102 can operate without the external crystal oscillator (crystal -less operation) and still provide a highly stable reference frequency /REF- It can be appreciated that a TIO 102 in accordance with the present disclosure is robust against aging and hence_7 generally does not vary over time.

[0032] The discussion will now turn to a description of the frequency generator 104 in accordance with various aspects of the present disclosure. The frequency generator 104 may use any suitable frequency generator design. Merely to illustrate this point, FIGURE IB for example, shows in some aspects that a frequency generator 104 may be based on a phase locked loop (PLL) 124. The PLL 124 may include a voltage controlled oscillator (VCO) 22 that produces the output signal 114 of oscillator 100. The output frequency of the VCO 22 may be controlled by a VCO control signal provided to the VCO 22. A feedback signal may be produced using a fractional divider 24 to divide the output frequency four by multiplier 116. A phase detector circuit 26 may produce an error signal based on whether the feedback signal leads or lags the reference frequency /REF (e.g., from TIO 102). The error signal may be filtered by a low pass filter 28 to produce the Vc control signal, which is used to control VCO 22 to produce the output signal 114.

[0033] One of ordinary skill will appreciate that frequency generator 104 may be realized with other designs. In some aspects, for example, the frequency generator 104 may be based on a digital frequency locked loop (DFLL). In some aspects, a DFLL may be more suitable over a PLL because the DFLL can be more compact and thus may be implemented in a reduced silicon area. A DFLL, by virtue of its digital nature, can also generate an output signal 114 having a frequency of arbitrary precision; for example, by designing the DFLL with a sufficient number of bits (resolution). In other aspects, a frequency lock loop (FLL) may be use to implement the frequency generator 104, and so on.

[0034] Frequency generators, whether a PLL, DFLL, and so on, typically include low pass filtering as part of its operation to filter high frequency artifacts that may arise during operation of the frequency generator. The filtering provided in frequency generators can relax certain design aspects of the TIO 102. For example, the jitter performance and power supply rejection performance requirements of the TIO 102 can be lowered in order to simplify the design of the TIO 102. The noise that can arise in the TIO 102 due to these lowered requirements can be filtered out by the frequency generator 104. On the other hand, in accordance with the present disclosure, the TIO 102 can provide a temperature invariant reference frequency / _REF - This fact can be used to relax constraints in the frequency generator 104 to design for temperature stable operation.

[0035] FIGURE 2 shows a block diagram of a circuit 200 in accordance with the present disclosure. The circuit 200 may include a bandgap reference (bias) core 220 and circuitry 240. In accordance with the present disclosure, the bandgap reference core 220 may operate to provide a temperature independent bandgap voltage (V _REF ) and a temperature independent bandgap current (I _REF )- Accordingly, most circuit

imperfections and variations (e.g., due to temperature) are tracked out; i.e., changes in the bandgap voltage and the bandgap current track each other. The circuitry 240 may be characterized in that an output 260 of the circuitry 240 may realize the ratio VREF

REF

which has a unit of resistance. The ratio, which may therefore be referred to as a "bandgap resistor," is also temperature independent. Because the output 260 of circuit 200 may be expressed in terms of this ratio called bandgap resistor, the output 260 is temperature independent. An instance of the circuit 200 is shown in FIGURE 2 A, although circuit 200 may be any circuit whose operation can be expressed or otherwise characterized in terms of bandgap resistor ratio, and thus can exhibit temperature independent operation. It is noted that the term "bandgap" typically refers to a process, supply voltage, and temperature (PVT) voltage. As used herein, the term "bandgap" in bandgap resistor may be used to signify only voltage and temperature independence. It is also noted that "temperature independent" is not meant to require absolute independence. A small amount of temperature dependency is contemplated by the term "temperature independent."

[0036] FIGURE 2 A shows a high level block diagram of TIO 102 (FIGURE 1) in accordance with the present disclosure. In some aspects, the TIO 102 may be logically viewed as having two functional sections: a bandgap reference (bias) core 202 and an oscillator section 204. As will be explained in more detail below, the bandgap reference core 202 may operate to provide a temperature independent bandgap voltage (V _REF ) and a temperature independent bandgap current (I _REF ). The oscillator section 204 may output a frequency / _REF that can be expressed in terms of the ratio— , referred to as

I REF

the bandgap resistance. In accordance with the present disclosure, the bandgap voltage and bandgap current may be generated from the same bias core. Accordingly, most circuit imperfections and variations (e.g., due to temperature) are tracked out. A more detailed description of the bandgap reference core 202 and oscillator section 204 will now be described.

[0037] FIGURE 3 shows details of a bandgap reference core 302 and an oscillator section 304 in accordance with some aspects of the present disclosure. As explained above the bandgap reference core 302 may generate both a bandgap voltage {V _REF ) and a bandgap current (I _REF ) to ensure that circuit imperfections and variations get tracked out. In some aspects, the bandgap reference core 302 may include a complementary to absolute temperature (CTAT) current source 314 and a proportional to absolute temperature (PTAT) current source 312. The CTAT core 314 may generate a current IcTAT that is sensitive to or otherwise varies with changes in temperature. As the name suggests, IcTAT may vary inversely with temperature; in other words, I _CT A _T generally decreases linearly as temperature increases and vice versa. Similarly, the PTAT core 312 may generate a current I _PT A _T that is also sensitive to or otherwise varies with temperature, but in opposite relation to IC _T A _T - In other words, whereas IC _T A _T may vary inversely with temperature, I _PT A _T may vary directly with temperature; I _PT A _T generally increases linearly as temperature increases and vice versa. [0038] The bandgap reference core 302 may include a first current summing circuit 316 (e.g., a first current summer) to produce a first summed current I] comprising a first combination of I _PT A _T and I _CT A _T - In some aspects, for example, the summing circuit 316 may include current generators that mirror IC _T A _T and I _PT A _T to produce respective mirrored currents IC _T A _TM and I _PT A _TM - The IC _T A _TM and IpTA currents may be summed at node A to produce Ij.

[0039] The bandgap reference core 302 may include a second current summing circuit 318 (e.g., a second current summer) to produce a second summed current I _REF comprising a second combination of I _PT A _T and I _CT A _T , and may be referred to as a bandgap current.

[0040] In some aspects, for example, the summing circuit 318 may include current generators that mirror IC _T A _T and I _PT A _T to produce respective mirrored currents IC _T A _TM and Ip _TA - The summing circuit 318 may further include a variable current generator that mirrors I _CT A _T to generate an additional current. In some aspects, the additional current may comprise a portion of I _CT A _T - For example, the summing circuit 318 may produce a scaled (weighted) mirrored CTAT current ICTATW- The ICTATM, IPTATM, and ICTATW currents may be summed at node B to produce I _REF - This aspect of the present disclosure will be discussed in more detail below.

[0041] FIGURE 3 shows that the mirrored currents IC _T A _TM and I _PT A _TM generated in the summing circuit 316 are the same as the mirrored currents IC _T A _TM and I _PT A _TM generated in the summing circuit 318. It will be appreciated, however, that in some aspects, these mirrored currents may be scaled differently. In general, the mirrored CTAT current generated in summing circuit 316 may be the same (as in FIGURE 3) or different from (greater than or less than) the mirrored CTAT current generated in summing circuit 318. Similarly, the mirrored PTAT current generated in summing circuit 316 may be the same (as in FIGURE 3) or different from (greater than or less than) the mirrored PTAT current generated in summing circuit 318. The remaining figures and following discussion and analyses will assume without loss of generality that the mirrored currents I _CT A _TM and Ip _TA are equal, in order to avoid overcomplicating the discussion.

[0042] In some aspects, the oscillator section 304 may be based on an RC ramp circuit to generate its output V _OUT - The oscillator section 304, for example, may include a resistor R and a capacitor C. The resistor R may be connected to the summing circuit 316 and driven by Ij to produce a voltage VREF across resistor R at node A. The capacitor C may be connected to switches 326a, 326b. In a first configuration (e.g., FIGURE 3 A), the capacitor C may be connected to the summing circuit 318 via switch 326a to be charged by IREF to produce a voltage Vc across the capacitor C. In a second configuration (e.g., FIGURE 3B), capacitor C may be disconnected from the summing circuit 318 and discharged, for example, by shorting capacitor C to ground potential via switch 326b.

[0043] The oscillator section 304 may include a comparator 322 to compare the voltage VREF across resistor R and the voltage Vc across capacitor C to produce an output VOUT- The output VOUT may flip between a HI output level and a LO output level as the capacitor C cycles between the charging and discharging configurations. In some aspects, the output VOUT of comparator 322 may serve as the reference frequency REF of the TIO 102.

[0044] The oscillator section 304 may include a phase generator 324 to control the OPEN and CLOSED state of switches 326a, 326b. The phase generator 324 may use the output our to generate switch control signals CH, fer to control the OPEN and CLOSED state of respective switches 326a, 326b. The switches 326a, 326b may operate in opposing (non-overlapping) phases; when one switch (e.g., 326a) is in the OPEN state, the other switch (e.g., 326b) is in the CLOSED state and vice versa.

[0045] Operation of the oscillator section 304 can be explained with reference to the timing diagrams shown in FIGURE 3C. Consider the charging cycle at time t=0, where the output VOUT of comparator 322 is LO and CH is HI (switch 326a is CLOSED) and RST is LO (switch 326b is OPEN). In this state, the capacitor C is configured for charging by IREF (e.g., FIGURE 3 A). The voltage Vc across the capacitor C begins to rise as charge accumulates in capacitor C. The voltage Vc continues to rise until at time t] when the voltage Vc becomes equal to the voltage VREF across resistor R and trips the comparator 322. At time tj, the output VOUT of comparator 322 goes HI, which in turn can flip ^o _/ to LO (opens switch 326a) and ^asr to HI (closes switch 326b). In this state, the capacitor C is configured for discharging (e.g., FIGURE 3B) by disconnecting IREF and shorting capacitor C to ground potential. The discharge time (t ₂ - tj) of capacitor C should be short and is exaggerated in the figure to highlight the relative transitions of VOUT, <I>CH, and (/>RST- This sequence of charging and discharging capacitor C may repeat to generate oscillations at the output V _OU In some implementations, when Vc is discharged at time t ₂ the switch can be reconfigured φαπ equal to HI and (/> _R S _T equal to LO so that the next charging cycle can begin. The oscillation period may not be affected by the time when the comparator output falls, so long as the comparator output falls prior to when it is next triggered (e.g., when the next ramp of Vc reaches a next trip point V _REF )-

[0046] In the single capacitor configuration of FIGURE 3, the discharge time (t ₂ - tj) is part of the period of oscillations. This discharge time can be very short and hence negligible relative to the oscillation period. Alternatively, charging and discharging two grounded capacitors (instead of one) can occur to exclude the discharge time from the period of oscillations. Similarly, propagation delay through the comparator 322 and phase generator 324 can be made very short relative to the period of oscillations or tracked out through an additional feedback loop so their variation with temperature and supply can be neglected. Thus, in some aspects of the disclosure, the period is

substantially set only by the capacitor charging time while the discharge time and comparator propagation delays are excluded from the period analysis or setting.

[0047] Referring to FIGURES 3 and 3C, the period T of the oscillations in V _OUT may be determined using the capacitor charging equation, which can be expressed as: i ^{= C} - _> Eqn. (1)

At where i is I _REF , the charging current into capacitor C,

Δν is the voltage V _REF across resistor R, and

At is the time (period T) it takes to charge capacitor C to the level of V _REF - Solving for At can produce the expression: K ^-C , Eqn. (2)

I REF where Jis At and represents the period of oscillations, and

V _REF depends on I] and R.

In other words, the period of oscillations is proportional to a ratio of V _REF to I _REF -

[0048] FIGURE 4 shows details of the bandgap reference core 302 (FIGURE 3) in accordance with some aspects of the present disclosure. As explained above, the bandgap reference core 302 includes a CTAT core 314 and a PTAT core 312. Circuit designs for PTAT and CTAT cores are known. The specific PTAT and CTAT core design disclosed herein is merely an illustrative example to explain aspects of the present disclosure. Persons of ordinary skill will understand that other suitable PTAT and CTAT core designs can be adapted in accordance with the present disclosure. The disclosed CTAT core 314 and a PTAT core 312 generate respective CTAT and PTAT currents. Persons of ordinary skill will appreciate that in some aspects of the present disclosure, the bandgap reference core may comprise CTAT and PTAT cores configured to produce the duals of CTAT and PTAT currents, namely, CTAT and PTAT voltages.

[0049] For example, the bandgap reference core generates the CTAT and PTAT voltages, converts them to currents through resistors and sums them in the current domain using two current ratios. In some implementations, the first current ratio is such that it generates the bandgap voltage when converted back to a voltage using a load resistor and the second current ratio is such that it generates the bandgap current. It is noted that "ratio" means that a value varies directly relative to one parameter and is inversely proportional to another parameter.

[0050] In some aspects of the disclosure, the bandgap reference core may be configured to be the dual of the above. For example, the bandgap core generates the CTAT and PTAT voltages and sums them in the voltage domain using two voltage ratios. For example, the first voltage ratio is such that it generates the bandgap voltage and the second voltage ratio is such that it generates the bandgap current when converted to a current using a load resistor. An example of this dual implementation is a switched-capacitor based bandgap circuit where capacitors ratios are used to set the voltage ratios.

[0051] The PTAT core 312 may include two p-n junctions. In some aspects, for example, the p-n junctions may be realized with diode-connected bipolar junction transistors (BJTs) QDI, QD2 of different sizes, where the p-n junctions are the base- emitter junctions of QDI and Q _D2 - It will be appreciated that in some aspects, devices other than BJTs may be used to create the p-n junctions (e.g., diodes).

[0052] In some aspects, the PTAT core 312 may include a self-biased circuit comprising an opamp 404 and PMOS devices M2 and M3. A PTAT current I _PTAT may be generated by forcing a voltage difference AV _BEI between the p-n junction potential (e.g., base-emitter voltage, V _BEI ) of QDI and the p-n junction potential (e.g., base-emitter voltage, V _BE2 ) of QD2 across resistor Ri. The voltage V _Y at one input (e.g., non-inverting input) of the opamp 404 comprises the sum of the p-n junction potential V _BE2 of QD2 and the voltage Vm across resistor Ri. The voltage Vx at the other input (e.g., inverting input) of opamp 404 is the p-n junction potential V _BEI of QDI- The PMOS devices M2 and M3 mirror I _PT A _T down the F branch (e.g., first circuit branch) and the V _Y branch (e.g., second circuit branch). The opamp 404 uses the difference between voltages Vx and V _Y to produce a bias voltage vbiasp to bias M2 and M3 such that the flow of I _PT A _T in both the F branch and the V _Y branch equalizes the voltages V _x and V _Y . The difference AV _BE between V _BEI and V _BE2 varies in direct proportion to temperature (e.g., 502, FIGURE 5); AV _BE increases with an increase in temperature and vice versa (e.g., 502, FIGURE 5). Because AV _BE is typically more strongly PTAT (relative to resistor RI), I _PT A _T is also directly proportional to temperature.

[0053] In some aspects, the CTAT core 314 may include opamp 402 and PMOS device Ml . A CTAT current I _CT A _T may be generated by forcing the p-n junction potential V _BEI of QDI across resistor R ₂ . In some aspects, resistor R ₂ may be a variable resistor that can be adjusted to make V _REF a bandgap voltage. The voltage V _R at one input of opamp 402 is the voltage across resistor R ₂ , and the voltage at the other input of opamp 402 is the voltage Vx, namely the p-n junction potential V _BEI - The PMOS device Ml controls I _CT A _T in the V _R branch (e.g., third circuit branch). The opamp 402 uses the difference between voltages V _R and Fx to generate a bias voltage vbiasc to bias Ml such that the flow of I _CT A _T in both the V _x branch and the V _R branch equalizes the voltages V _x and V _R . The voltage V _BEI varies inversely with temperature; V _BEI decreases linearly with an increase in temperature and vice versa (e.g., 504, FIGURE 5). Accordingly, I _CT A _T also varies inversely with temperature. Because V _BEI is typically more strongly CTAT (compared to resistor R2), I _CT A _T also varies inversely with temperature.

[0054] Continuing with FIGURE 4, the bandgap reference core 302 may include summing circuit 316. In some aspects, the summing circuit 316 may include a PMOS device M4 to mirror the CTAT current I _CT A _T and a PMOS device M5 to mirror the PTAT current I _PT A _T - For example, the PMOS device M4 may be biased using the bias voltage vbiasc generated by the CTAT core 314 to produce a mirrored CTAT current IcTATm- Similarly, the PMOS device M5 may be biased using the bias voltage vbiasp generated by the PTAT core 312 to produce a mirrored PTAT current I _PT A _TM - The mirrored currents IC _T A _TM and I _PT A _TM can be summed or otherwise combined at node A in the summing circuit 316 to produce the current.

[0055] The bandgap reference core 302 may include summing circuit 318. In some aspects, the summing circuit 318 may include a PMOS device M7 to mirror the CTAT current I _CT A _T and a PMOS device M8 to mirror the PTAT current I _PT A _T - For example, the PMOS device M7 may be biased using the bias voltage vbiasc generated by the CTAT core 314 to produce a mirrored CTAT current I _CT A _TM - Similarly, the PMOS device M8 may be biased using the bias voltage vbiasp generated by the PTAT core 312 to produce a mirrored PTAT current IpTATm- The summing circuit 318 may further include a variable current generator that mirrors I _CT A _T to produce a scaled (weighted) mirrored CTAT current I _CT A _TW (explained below), which represents a portion of I _CT A _T - In some aspects, for example, the variable current generator may include a variable PMOS device M6 having multiple fingers that can be programmatically selected. In other aspects, the variable current generator may include a variable resistor R _x (inset) connected in series with a fixed M6. The mirrored currents IC _T A _T W, IC _T A _TM , and IpTATm can be summed or otherwise combined at node B to produce the I _REF current.

[0056] As shown in FIGURE 4, in some aspects the bandgap reference core 302 may be realized using PMOS devices Ml - M8. It will be appreciated that in other aspects, the devices Ml - M8 may be realized using MOS devices. For the remaining figures and the following discussion, devices Ml - M8 can be assumed to be PMOS devices without loss of generality.

[0057] Referring again to FIGURE 3, in accordance with the present disclosure, capacitor C in the oscillator section 304 can be made temperature invariant. For example, fringe capacitors have a near-zero temperature coefficient because their capacitance is a function of geometric and material properties that vary little with temperature. Metal-oxide-metal (MOM) capacitors, for example, can have zero tempco. Temperature coefficient ("tempco") generally refers to a factor that relates a change in a quantity (e.g., capacitance) to a change in temperature, and can be a positive value or a negative value. A positive tempco indicates the quantity is directly proportional to temperature (e.g., capacitance increases as temperature increases and vice versa), and a negative tempco indicates the quantity varies inversely with temperature (e.g., capacitance decreases as temperature increases and vice versa). A zero tempco indicates the quantity does not change (is invariant) with temperature.

[0058] By contrast, the resistor R in the oscillator section 304, in accordance with the present disclosure, may be realized using a temperature sensitive (non-zero tempco) resistor. Depending on the particular materials used, the resistor R may have PTAT behavior (resistance varies directly with temperature) or CTAT behavior (resistance varies inversely with temperature). Relaxing the temperature constraint on resistor R allows for a simpler and lower cost design resistor as compared to a design that imposes a requirement of temperature invariance; e.g., a zero tempco resistor may be realized by combining resistors having equal and opposite tempcos, possibly adding complexity to the fabrication process, and the like. In some technologies, it may not be practical or possible to make a temperature invariant resistor. For example, FinFET fabrication generally cannot provide resistor designs that have opposite tempcos and so the approach of creating a zero tempco resistor using resistors with opposite tempcos may not be available.

[0059] As explained above, the period T (and hence the frequency) of / is primarily set by the RC product as indicated in Eqn. 2 (Ij and IREF are based on the PTAT and CTAT cores 312, 314). If a temperature sensitive resistor is used, then temperature variations will affect resistor R, which in turn can result in corresponding fluctuations inREF-

[0060] In accordance with the present disclosure, summing circuit 316 may be configured to generate a current I] having a temperature sensitivity that is in opposite relation to the temperature sensitivity of resistor R. For example, if resistor R is PTAT, then I] can be CTAT so that an increase in resistance due to a temperature increase can be matched by a decrease in Ij. Conversely, if resistor R is CTAT, then I] can be PTAT so that a decrease in resistance due to a temperature increase can be matched by an increase in Ij. In other words, Ij may be characterized with a tempco (a) that is equal to but opposite in sign to the tempco (-a) of the resistor R. Thus, an x% change in the resistance of resistor R in one direction (increase or decrease) can be matched by an x% change in I] in the opposite direction. Accordingly, when I] is driven into resistor R, the resulting voltage V _RE F across resistor R can be temperature invariant. Without loss of generality, the configuration depicted in the figures (e.g., FIGURES 3, 4) assume resistor R is CTAT, and so I] is PTAT.

[0061] In accordance with the present disclosure, the summing circuit 318 may generate an I _REF that is temperature invariant. The summing circuit 318 may produce a current IREF that is the sum of the mirrored currents ICTATM, ICTATW, and IPTATM- AS explained above, in accordance with the present disclosure I], which is the sum of I _CT A _TM and IpTATm, may vary with temperature. For example, as noted above, the configuration shown in FIGURE 4 assumes resistor R is CTAT and so I] is PTAT. Accordingly, the sum of the mirrored currents I _CT A _TM and IpTATm in the summing circuit 318 is also PTAT. Accordingly, in some aspects, additional CTAT current may be added to make I _REF a bandgap current. For example, the summing circuit 318 may generate a current I _CT A _TW that is scaled so as to offset the PTAT behavior of the sum of the mirrored currents IcTA and IpTA in summing circuit 318, resulting in an I _REF current that is temperature independent.

[0062] Referring to FIGURE 4 A, in other aspects, the bandgap reference core 302 may be configured for a resistor R that is PTAT. Accordingly, I] would be CTAT, and so the sum of the mirrored currents IcTATm and I _PT A _TM in the summing circuit 318 would also CTAT. In accordance with the present disclosure, the summing circuit 318 may add extra PTAT current to make I _REF a bandgap current. For example, summing circuit 318 may include a variable PMOS device M9 to generate a weighted mirrored PTAT current I _PT A _T W that is scaled so as to offset the CTAT behavior of IcTATm + I _PT A _TM in summing circuit 318, resulting in an I _REF current that is insensitive to temperature. The remaining discussion, however, can assume the configuration of FIGURE 4 without loss of generality.

[0063] Referring to FIGURE 4B, a more general configuration of the bandgap reference core 302 may include variable PMOS devices M ₄ - M ₈ to generate the bandgap voltage V _REF and bandgap current I _REF - The bandgap reference core 302 may include degeneration resistors Rs to suppress current mismatch in the PMOS devices Mi - M ₈ . One or more of the degeneration resistors RS may be programmable or variable to adjust mirroring ratios. [0064] Recall from above that the period T of reference frequency f _REF (output of TIO 102) can be expressed in terms of V _REF and I _REF . Eqn. 2 above, for example, expresses this relation as follows:

_T∞ iEF_ _C

As explained, the capacitor C can be a temperature invariant device. Likewise, a temperature invariant V _REF and a temperature invariant I _REF can be generated. Since the period T can be determined based on terms (V _REF , I _REF ) that are temperature invariant, the TIO 102, in accordance with the present disclosure, can provide a reference frequency f _RE F that is also temperature invariant. In particular, a temperature invariant f _RE F can be advantageously produced without imposing the constraint that the design employs a temperature invariant resistor R. This and other advantages are discussed further below.

[0065] The discussion will now continue with a more qualitative description of operation of the TIO 102, with reference to FIGURES 3 and 4 and with an emphasis on operation of the bandgap reference core 302 in accordance with aspects of the present disclosure. The equations and analyses present below generally represent first-order approximations of actual circuit behavior, and are intended to be illustrative of circuit operation in accordance with the present disclosure.

[0066] From Eqn. 2 , the period T of the reference frequency f _RE F from TIO 102 may be expressed as:

I REF

The expression may be rewritten as:

T oc R _REF C , Eqn. where

R _REF = ^J f^ . Eqn.

IREF

Given that = I _} R , R _REF may also be expressed as: ^R REF = ^R - · Eqn-

IREF

As noted above, the ratio RREF may be referred to as a "bandgap resistor." Equation 3 therefore expresses an operation of TIO 102 in terms of the bandgap resistor ratio. In particular, the bandgap resistor RREF characterizes an operation of the TIO 102, namely RREF in combination with the capacitor C sets an operating frequency of the TIO 102.

[0067] As noted above, while capacitor C may be made temperature invariant, it may be not desirable (or practical) to impose a requirement on resistor R that it also be temperature invariant. Accordingly, in accordance with the present disclosure, resistor R may be allowed vary with temperature. Resistor R may be modeled as:

R = R ₀ (l + aAT) , Eqn. where R is the resistance at a temperature J (e.g., circuit operating temperature),

R ₀ is the resistance at a reference temperature T ₀ (e.g., room temperature), a is a temperature coefficient of resistor R, and

ΔΤ is T- T ₀ .

[0068] As explained above, the currents and IREF are derived from I _PT AT and ICTAT- Referring to FIGURE 4, I _PT AT may be expressed in terms of resistor Ri in the following derivation. By operation of opamp 404:

where V _B EI and V _B E2 are the p-n junction potentials of Q _D i and Q _D2 , respectively, and

VRI is the voltage across resistor Ri.

The voltage VRI, in turn, can be expressed as:

Voltage VRI can also be expressed in terms of IPTAT as:

VRI = ^J PTAT ^R i ^E q ⁿ - ( ⁹ )

Combining Eqns. 8 and 9 produces the following expression for IPTAT in terms of Ri: The CTAT current I _CT A _T may be similarly expressed in terms of resistor R ₂ as follows:

V _R2 = V _BE1 Eqn. (l l) VR2 ^{= i} CTAT ^{x R} 2 Eqn. (12)

I _CT A _T = ^ - Eqn. (13)

The mirrored currents I _CT A _TM and IpTATm in the summing circuits 316, 318 may be represented by Eqns. 10 and 13, respectively.

[0069] The current I] from summing circuit 316 comprises I _CT A _TM + I _PT A _TM , which may be expressed using Eqns. 10 and 13 as:

I ₁

where W] is a weighting term.

A mentioned above, I _CT A _T and I _PT A _T may be weighted (e.g., in the respective PTAT and CPTAT cores 312, 314) in accordance with the present disclosure such that the sum of IcTATm and I _PT A _TM in summing circuit 316 produces an I] having the temperature

properties described above in relation to resistor R, namely that varies with respect to temperature by the same amount as does resistor R, but in opposite relation. It will become apparent in the discussion below that this property of Ij can be achieved by setting the weighting term w ]. In some aspects, I _CT A _T and I _PT A _T may be weighted relative to each other by applying the weighting term wj to the I _CT A _T current, as shown in Eqn. 14. It will be appreciated that in other aspects, the weighting term w ] may be applied to the I _PT A _T current.

[0070] The current I _REF from summing circuit 318 comprising IC _T A _TM + IC _T A _T W + I _PT A _TM may be expressed using Eqns. 10 and 13 :

J - _w ^V BEl , V _BE

REF ^{~ W} 2 +

R R _j

Eqn. (15) where w ₂ is a weighting term >1.

In accordance with the present disclosure, the term w ₂ ^mav represent the combined current in the I _CT A _TM and I _CT A _TW branches in the summing circuit 318. [0071] Substituting Eqns. 14 and 15 into Eqn. 5 yields: e _f = R n ⁿ ₂ ⁱ lV ^B _B ^E _E ¹ ₁ ⁺ +ZAV ^B _B ^E _E ^{> Ε} ¾ ^η· ( ¹⁶ ) where n, = w, .

[0072] Substituting R in Eqn. 16 with the expression in Eqn. 6 yields:

R _ref = R ₀ (l + aAT)^, Eqn. (17) where V ₁ = ny _BE1 + AV _BE , and

V ₂ = n ₂ V _BEl + AV _BE .

[0073] Referring for a moment to FIGURE 5, persons of skill will understand that the slope characteristics of V _BEI and AV _BE with respect to temperature are predictable and well understood. For example, AV _BE may be represented (as a first-order

approximation) by a straight line plot 502 relating voltage vs. temperature. Similarly, V _BEI may be represented by a straight line plot 504. With respect to Eqn. 17, the _j V _BE1 and n ₂ V _BE1 terms may also be represented by straight lines similar to plot 504, except that the multiplication factors n ₂ alter the slopes and the intersection points on the voltage axis. The straight line plot 512 in FIGURE 5 represents the sum of V _BEI and AV _BE - Accordingly with respect to Eqn. 17, the Vi and V ₂ terms may also be represented by straight lines similar to plot 512, with the multiplication factors n n ₂ taken into consideration.

[0074] The straight line representations for Vi and V ₂ can be normalized to respective nominal voltages J ⁷ / and V ₂ ° at a reference temperature T ₀ (e.g., room temperature). Vi and V ₂ can be expressed in terms of change relative to their nominal voltages (J ⁷ / and V ₂ ° ) vs. changes in temperature (Δ7) relative to the reference temperature T ₀ . Accordingly, each of the expressions for Vj and V ₂ in Eqn. 17 can be expressed in terms of a fractional change from the nominal voltages J ⁷ / and V ₂ ° :

Eqn. (18)

V ₂ = V ₂ ° (l ₊ P ₂ AT) , where J ⁷ / and J ⁷ are nominal voltages at the reference temperature T ₀ ,

βι and β ₂ are effective temperature coefficients, and

AT is the temperature difference (T-T ₀ ).

Equation (18) relating to V ₂ , for example, can be expanded as follows: ν ₂ = (ν ₂ ° +ν ₂ °β ₂ Ατ) Eqn. (19)

It can be shown that the βι and /¾ terms represent the slopes of the respective straight line plots (e.g., FIGURE 5) that represent (n _j V _BE1 + AV _BE ) and (n ₂ V _BE1 + AV _BE ) normalized to respective nominal voltages J ⁷ / and V ₂ ° . Substituting Eqn. 18 into Eqn.

17 yields:

where R _REF I ^' S computed for a temperature T (e.g., circuit operating temperature), and

Ro is the resistance of resistor R (Eqn. 6) at the reference temperature To, a is a temperature coefficient of resistor R, and

AT is the temperature difference (T- AT).

Setting βι equal to 0 and /¾ equal to a, reduces Eqn. 20 to:

which is an expression that contains no dependency to changes in temperature and is thus temperature invariant. Recall from Eqn. 4 that R _REF can be expressed as:

REF

R REF - _j

!REF which is an expression of Ohm's law for resistors. R _REF therefore represents a resistive term, and because R _REF is temperature invariant as shown above, R _REF may be referred to as a "bandgap resistor." Tying back to the reference frequency J _REF in FIGURE 3, Eqn. 3 shows that the period T ΟΪ/ _REF may be expressed in terms of this bandgap resistor:

T R _REF .

Since the bandgap resistor term is temperature invariant and the capacitor C is

temperature invariant, the resulting period T is also temperature invariant.

[0075] The discussion will now turn to a description that relates the βι and /¾ terms to circuit elements comprising the TIO 102. A derivation will be described for /¾ with the understanding that a similar derivation can be made for /¾.

[0076] Consider first the βι term. Recall from Eqns. 16 and 17 that V] is defined as:

Vi = niV _BE i + V _BE , Eqn. (22) where n ₁ = w ₁ —^- .

R ₂

[0077] Referring to FIGURE 5, V _BEI and AV _BE can be represented (as a first-order approximation) by the straight line equation y=mx+b as follows:

V _BE1 : y = _mi x x + V _a

Eqn. (23)

AV _BE : y = m ₂ x x + V _H , where mj is the slope of the V _BEI line, and

m ₂ is the slope of the AV _BE line.

Using Eqns. 22 and 23, the sum Vj can similarly be represented by a straight line equation:

V ₁ : y = m ₃ x x + V _c , Eqn. (24) where m ₃ is the slope of the Vj line, which can be expressed as w ₁ —m ₁ + m ₂ .

^R 2

Normalizing Vj, the βι term may then be expressed as:

[0078] As explained above in connection with Eqns. 20 and 21, setting βι = 0 can generate a Vi that is temperature invariant. Solving Eqn. 25 for βι = 0 results in the following:

The w i weighting term can be set to one since the term in this case only serves to scale the resistor values Rl, R2. Eqns. 5, 14, and 17 show that V _REF ∞ Vi. Therefore, in accordance with the present disclosure, the ratio of resistors Rj and R ₂ in bandgap reference core 302 may be set according to the ratio of the slopes of V _BEI and AV _BE to generate I _CT A _T and I _PT A _T currents that are weighted such that when the sum of I _CT A _T and I _PT A _T are driven into resistor R, the voltage V _REF across resistor R can be temperature invariant.

[0079] Consider next the /¾ term. Recall from Eqns. 16 and 17 that V ₂ is defined as:

V ₂ = n ₂ V _BEL + AV _E Eqn (27) where n ₂ = w ₂

R ^v ,2

[0080] Referring to FIGURE 5, V _BEI and AV _BE can be represented (as a first-order approximation) by the straight line equation y=mx+b as shown in FIGURE 23. where mj is the slope of the V _BEI line, and

m ₂ is the slope of the AV _BE line.

Using Eqns. 27 and 23, the sum V ₂ (like Vi) can similarly be represented by a straight line equation:

V ₂ : y = m ₃ x x + V _C , Eqn. (28) From equation 27, 23 and 28, V ₂ = w ₂ — (m _l x x + V _a ) +m ₂ x x + V _B

^R 2

R R

K ₂ K ₂ where, in this case, m ₃ is the slope of the V ₂ line, which can be expressed as w ₂ — ^! -m _l + m ₂ .

As noted, it can be shown that the βι and /¾ terms represent the slopes of the respective straight line plots (e.g., FIGURE 5) that represent ny _mx + AV _BE ) and (n ₂ V _BEl + AV _BE ) normalized to respective nominal voltages J ⁷ / and V ₂ ° .

Based on equation 18 V ₂ = w ₂ — ί- x V _a + V _b Eqn. (29)

[0081] Consider next the /¾ term. Similar to Eqn. 25, normalizing /¾, the /¾ term may be expressed as:

[0082] As shown in Eqn. 21, setting /¾ = a allows for the coefficient terms (l + AT) and (l + β ₂ ΔΤ) to cancel out, thus generating a V ₂ that changes with resistor R as temperature changes. Because the Ri and R ₂ resistors have been solved according to Eqn. 25, they are deemed fixed quantities. Accordingly, Eqn. 30 may be solved for the w ₂ weighting term where /¾ = a, which results in the following:

R V° - m

w ₂ =— x— - . Eqn. (31)

R _j m ₁

Substituting for V ₂ from equation 29 and solving for w ₂ , we get

Because all the quantities on the right hand side are known in equation 32, the

appropriate w ₂ can be computed for a given design.

Referring to FIGURE 4, in accordance with the present disclosure, the w ₂ weighting term may be used to program the variable resistor R _x to generate I _CT A _TW - Conclusion

[0083] In accordance with the present disclosure, a voltage and temperature stable oscillator is presented. A calibration engine provides correction for process variations, resulting in an oscillator that is "PVT" stable.

[0084] Various aspects of the present disclosure ensure against fluctuations due to circuit imperfections and process variation. For example, traditional bandgap designs focus on building a voltage (or current) with very high absolute precision. Absent advanced design techniques, this precision is limited by various imperfections, such as inherent nonlinearity of V _BE with temperature, process dependent curvature artifacts, offsets/mismatch, etc. In order to achieve sub 1% accuracy, more advanced schemes (like non-linear curvature compensation, chopping, etc.) are incorporated into a design, typically at the cost of complexity, area, and power.

[0085] In contrast, aspects of a bandgap reference core 302 (FIGURE 4) in accordance with the present disclosure are based on building a high precision resistor (bandgap resistor, R _REF ), which is a ratio of a voltage (V _REF ) and a current (I _REF ) which can be re-arranged as a ratio of two voltages. From Eqns. 16 and 17, recall that: n _i V _BE1 + V _L

R BE

-REF ^_ R

B _E1 + AV ₁ BE

[0086] Since this expression relies on a ratio, the numerator and denominator do not need very high absolute precision or linearity, but rather should track each other as much as possible. Notice that this can be realized this by generating the two summed currents identically so that they track each other except to cancel the tempco of resistor R. This is an advantage of the bandgap reference core 302 giving it immunity to circuit imperfections that arise from the bandgap reference core 302.

[0087] In addition, because we can precisely set a zero tempco on the frequency (by canceling the resistor's tempco), we can also intentionally set a non-zero tempco to the output frequency using this approach. For example, it may be desirable to decrease the clock frequency when hot because downstream ICs typically run slower when hot. [0088] The above description illustrates various embodiments of the present disclosure along with examples of how aspects of the particular embodiments may be implemented. The above examples should not be deemed to be the only embodiments, and are presented to illustrate the flexibility and advantages of the particular

embodiments as defined by the following claims. Based on the above disclosure and the following claims, other arrangements, embodiments, implementations and equivalents may be employed without departing from the scope of the present disclosure as defined by the claims.