Abstract:
Precision integrated time reference circuits are disclosed. Preferred embodiments provide time reference circuits that are relatively insensitive to variations in process, supply, and temperature. A preferred embodiment of the invention is disclosed in which a relaxation oscillator according to the invention includes a reference voltage circuit configured to maintain a reference voltage in proportion to actual circuit resistance values. Aspects of the invention also include dynamic compensation for variations in temperature.

Description:
TECHNICAL FIELD 
   The invention relates to microelectronic circuitry and methods for implementing the same. More particularly, the invention relates to integrated time reference circuitry for implementation in monolithic ICs providing improved performance and limited output variation due to variations inherent in electronic components and processes. 
   BACKGROUND OF THE INVENTION 
   Time reference circuits are often used in the arts where periodic waveforms or pulses are required. Many factors can affect the accuracy of such circuits such as inherent variations in resistance, capacitance, and other properties of the circuit components themselves. Variations in electrical properties to due changes in temperature can further complicate matters. For example, relaxation oscillators are one type of time reference circuits commonly used in monolithic IC designs. The basic mechanism is to charge or discharge a capacitor either through an R-C network or with a constant current source, thus producing a periodic waveform output. The output frequency is inversely proportional to the sum of the charging and the discharging times, and the duty cycle depends on the ratio of the charging to discharging time. Relaxation oscillators can be generally classified as R-C relaxation oscillators or constant-current relaxation oscillators. Simplified conceptual circuit schematic diagrams of examples of R-C and constant-current relaxation oscillators and their outputs are shown in  FIG. 1A  (prior art) through  FIG. 2B . 
   Referring primarily to  FIGS. 1A  (prior art), and  1 B, an example of an R-C relaxation oscillator circuit  10  is shown. The thresholds of the Schmitt trigger  12  are V a  and V b . The hysteresis of the Schmitt trigger  12  is V a -V b . With the switch S 1  open, v o1 , rises exponentially toward V cc . When it reaches V b , it trips the Schmitt  12  and S 1  closes, v o1  then drops exponentially toward V L . V L  is as given by Equation 2. When v o1  reaches V a  the Schmitt trigger  12  changes state and switch S 1  is opened once again, repeating the previous cycle. The frequency of the R-C relaxation oscillator circuit  10  output VOUT 1  shown in  FIG. 1B  can also be described by Equations 1 thru 7. 
   
     
       
         
           
             
               
                 
                   tau 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 = 
                 
                   r 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   c 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 ) 
               
             
           
           
             
               
                 VL 
                 = 
                 
                   
                     Vcc 
                     . 
                     r 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     2 
                     / 
                     
                       ( 
                       
                         
                           r 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         
                           r 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 ) 
               
             
           
           
             
               
                 
                   tau 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         r 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                            
                         
                         ⁢ 
                         r 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       ) 
                     
                     . 
                     c 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 ) 
               
             
           
           
             
               
                 
                   t 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 = 
                 
                   tau 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1. 
                   ⁢ 
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         Vcc 
                         - 
                         
                           Va 
                           / 
                           Vcc 
                         
                         - 
                         Vb 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
                 ) 
               
             
           
           
             
               
                 
                   t 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 = 
                 
                   tau 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2. 
                   ⁢ 
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         Vb 
                         - 
                         
                           VL 
                           / 
                           Va 
                         
                         - 
                         VL 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
                 ) 
               
             
           
           
             
               
                 f 
                 = 
                 
                   
                     1 
                     / 
                     T 
                   
                   = 
                   
                     1 
                     / 
                     
                       ( 
                       
                         
                           t 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         
                           t 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
                 ) 
               
             
           
           
             
               
                 
                   1 
                   / 
                   f 
                 
                 = 
                 
                   r 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   c 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1. 
                   ⁢ 
                   
                     { 
                     
                       
                         ln 
                         ⁡ 
                         
                           ( 
                           
                             Vcc 
                             - 
                             
                               Va 
                               / 
                               Vcc 
                             
                             - 
                             Vb 
                           
                           ) 
                         
                       
                       + 
                       
                         
                           ( 
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               2 
                               / 
                               
                                 ( 
                                 
                                   
                                     r 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                   + 
                                   
                                     r 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                         . 
                         
                           ln 
                           ⁡ 
                           
                             ( 
                             
                               Vb 
                               - 
                               
                                 VL 
                                 / 
                                 Va 
                               
                               - 
                               VL 
                             
                             ) 
                           
                         
                       
                     
                     } 
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
                 ) 
               
             
           
         
       
     
   
   Now referring primarily to  FIGS. 2A  (prior art) and  2 B, an example of a constant-current relaxation oscillator circuit  20  is shown. It may be seen that the constant-current source oscillator  20  uses a current I 2  instead of a resistor (R 2  in  FIG. 1A ) to charge and discharge a timing capacitor C 2 . With I 2  cut off, I 1  charges C 2  towards V cc  until v o2  equals V a . Then the Schmitt trigger  22  output goes high and the current source I 2  is turned on. Assuming I 2 &gt;I 1 , I 2 −I 1  now discharges the capacitor until v o2  equals V b . The Schmitt trigger  22  then changes state again and turns off I 2  to repeat the cycle.  FIG. 2B  portrays an example of a waveform output from a constant-current oscillator such as in the circuit shown in  FIG. 2A  (prior art). 
   Commonly in monolithic designs, the only constant source available is a voltage V BG  generated from a band-gap reference. The current I BG  generated from a band-gap referenced voltage V BG  using an on-chip resistor R makes the current I BG  dependent on the variation of the resistor R. Equations 8 thru 13 describe the output frequency dependency of a constant-current source oscillator on the on-chip resistor R and capacitor C. 
   
     
       
         
           
             
               
                 
                   i 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 = 
                 
                   
                     Vbg 
                     / 
                     r 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
                 ) 
               
             
           
           
             
               
                 
                   i 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 = 
                 
                   
                     k 
                     . 
                     i 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   
                     ( 
                     
                       k 
                       &gt; 
                       1 
                     
                     ) 
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
                 ) 
               
             
           
           
             
               
                 
                   t 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 = 
                 
                   
                     ( 
                     
                       Vb 
                       - 
                       Va 
                     
                     ) 
                   
                   ⁢ 
                   c 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     1 
                     / 
                     i 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
                 ) 
               
             
           
           
             
               
                 
                   t 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         Vb 
                         - 
                         Va 
                       
                       ) 
                     
                     . 
                     c 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     1 
                     / 
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   ⁢ 
                   i 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   11 
                 
                 ) 
               
             
           
           
             
               
                 f 
                 = 
                 
                   
                     1 
                     / 
                     T 
                   
                   = 
                   
                     
                       1 
                       / 
                       
                         ( 
                         
                           
                             t 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           + 
                           
                             t 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       i 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1. 
                       ⁢ 
                       
                         
                           ( 
                           
                             k 
                             - 
                             1 
                           
                           ) 
                         
                         / 
                         
                           ( 
                           
                             
                               k 
                               . 
                               c 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1. 
                             ⁢ 
                             
                               ( 
                               
                                 Vb 
                                 - 
                                 Va 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   12 
                 
                 ) 
               
             
           
           
             
               
                 f 
                 = 
                 
                   
                     Vbg 
                     . 
                     
                       ( 
                       
                         k 
                         - 
                         1 
                       
                       ) 
                     
                   
                   / 
                   
                     ( 
                     
                       
                         k 
                         . 
                         r 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1. 
                       ⁢ 
                       c 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1. 
                       ⁢ 
                       
                         ( 
                         
                           Vb 
                           - 
                           Va 
                         
                         ) 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
                 ) 
               
             
           
         
       
     
   
   The frequency of a relaxation oscillator depends on the R-C product and also on the supply voltage if the threshold of the trigger is dependent on the supply voltage. Circuit techniques have been developed to make the trip points or Schmitt trigger thresholds supply-independent. One way known in the arts to make the trip points supply-independent is to use band-gap voltage as a reference for comparison to the voltage across the capacitor. 
   An example of the band-gap referenced approach is illustrated in  FIG. 3  (prior art). The relaxation oscillator circuit  30  of  FIG. 3  uses a band-gap referenced current i BG . The current i BG  is switched using two inverters INV 1 , INV 2  to charge two capacitors C 3 , C 4  alternately. The first capacitor C 3  is charged to V BG , after which it trips the first comparator COMP 1 . The current i BG  is then switched to charge the second capacitor C 4 . The output of the oscillator VOUT 3  is high while the first capacitor C 3  is charged, and it then goes low when the first comparator COMP 1  trips. When the voltage V 4  on the second capacitor C 4  reaches V BG , a second comparator COMP 2  trips, and the current i BG  is switched back to the first capacitor C 3 , and so on. Thus, a periodic waveform output VOUT 3  is obtained with a 50% duty cycle. The output frequency depends on how much time the current i BG  takes to charge the capacitors C 3 , C 4  to V BG . Note that V BG  is independent of power supply. It is known to use external trim to correct the output frequency when for the effects of variation in temperature and process. Table 1 gives an example of representative frequency variation of this circuit  30  with two trim bits used to trim the frequency. 
   
     
       
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
               Trim = 01 
               Trim = 01 
               Trim = 11 
             
             
               Supply 
                 
               NOMINAL 
               WEAK fre- 
               STRONG 
             
             
               V 
               TEMP 
               Frequency (MHz) 
               quency (MHz) 
               Frequency (MHz) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               1.65 
               −40 
               5.89 
               4.66 
               5.81 
             
             
               1.65 
               27 
               5.39 
               4.20 
               5.36 
             
             
               1.65 
               150 
               5.12 
               3.98 
               5.19 
             
             
               1.80 
               −40 
               5.78 
               4.52 
               5.72 
             
             
               1.80 
               27 
               5.34 
               4.16 
               5.32 
             
             
               1.80 
               150 
               5.11 
               3.97 
               5.17 
             
             
               1.95 
               −40 
               5.70 
               4.45 
               5.66 
             
             
               1.95 
               27 
               5.30 
               4.13 
               5.29 
             
             
               1.95 
               150 
               5.10 
               3.96 
               5.16 
             
             
                 
             
           
        
       
     
   
   As shown in Table 1, the frequency is independent of supply voltage V CC  because the charging current V BG  and the reference voltage V BG  do not change with supply voltage V CC . There is however, significant variation over temperature and process. Trim must be used to re-center the frequency over process, in the absence of which the frequency is as high as 7.6 MHz at the strong corner with supply being 1.65 V at cold temperatures. These variations are mainly due to variations in capacitor and resistor values. The resistor variation leads to variation in the constant current V BG  that charges the capacitors, e.g. C 3 , C 4 , and causes frequency variation at the output. The value of the capacitors may change with process, which also causes frequency variation. In this example, in the absence of trim the oscillator output frequency varies from 7.6 to 3.96 MHz while it is centered around 5.5 MHz, a variation of 3.6 MHz. 
   The frequency of relaxation oscillators used in monolithic designs depends on the resistors and capacitors used in their implementation. The output frequency therefore varies to the extent that the resistors and the capacitors vary over process and temperature, and due to changes in the supply voltage. Though the supply dependency may be overcome using techniques known in the arts, the variation over process persists unless external trim components are used. Due to these and other problems, methods and circuits for providing relaxation oscillators insensitive to variations in process, supply voltage, or temperature changes would be useful and advantageous in the arts. 
   SUMMARY OF THE INVENTION 
   A time reference circuit insensitive to internal variations in resistance, capacitance, and temperature, is provided. In general, the circuit is arranged so that variations in electrical properties of the components tend to cancel one another. In a preferred embodiment, a circuit of the invention uses a charging capacitor connected to a current source for charging. The charging current source has an inherent resistance variation. A reference voltage circuit is used for generating a reference voltage that varies in relationship to the resistance variation of the charging current source, thus canceling the resistance variation. The reference voltage circuit also has a gate capacitance variation which cancels the variation of the MOS capacitance of the circuit. The reference voltage circuit and charging current circuit are also preferably configured to have the same inherent temperature variation so that potential errors due to temperature tend to cancel one another. 
   In carrying out the principles of the present invention, in accordance with preferred embodiments thereof, preferred embodiments of the invention provide a relaxation oscillator circuit including a reference voltage circuit configured to maintain a reference voltage in proportion to actual circuit resistance values. 
   According to an aspect of the invention, a relaxation oscillator circuit embodiment of the invention includes a charging current generator for generating a charging current from a voltage. A reference voltage circuit is provided for generating a reference voltage inversely proportional to the resistance of the charging current generator. Examples of preferred embodiments of the invention also include an oscillation generator for generating an oscillating output voltage from the charging current. The oscillation generator of the invention further includes one or more capacitors for charging by charging current, and a circuit configured to compare the voltage across each capacitor to the reference voltage. A switch circuit is controlled by the comparison circuit in order to regulate charging and discharging the capacitors. 
   According to another aspect of the invention, a preferred embodiment of a relaxation oscillator circuit includes a charging current generator configured to dynamically compensate for variations in temperature. 
   According to another aspect of the invention, a monolithic relaxation oscillator circuit includes a charging current generator configured for dynamically compensating the charging current for variations in temperature. A reference voltage circuit is included for generating a reference voltage inversely proportional to the resistance of the charging current generator. An oscillation generator is placed for receiving the charging current and generating an oscillating output voltage. The oscillation generator includes one or more capacitors for charging by the charging current, and a comparing circuit for comparing the voltage across each capacitor to the reference voltage. A switching circuit controlled by the comparing circuit is operably coupled for charging and discharging each capacitor. 
   According to yet another aspect of the invention, a relaxation oscillator circuit according to an example of a preferred embodiment of the invention has a charging current generator configured to use a current proportional to absolute temperature for charging one or more capacitors. 
   According to another aspect of the invention, a relaxation oscillator circuit embodiment of the invention includes a reference voltage circuit having dual current mirrors for balancing the reference voltage proportional to the resistance of the charging current generator. 
   The invention has advantages including but not limited to providing robust relaxation oscillators with limited frequency variation due to their relative insensitivity to supply, process, or temperature effects. Additional advantages include the elimination of the need for external trimming. These and other features, advantages, and benefits of the present invention can be understood by one of ordinary skill in the arts upon careful consideration of the detailed description of representative embodiments of the invention in connection with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will be more clearly understood from consideration of the following detailed description and drawings in which: 
       FIG. 1A  (prior art) is a simplified conceptual schematic diagram representative of R-C relaxation oscillator circuits known in the arts; 
       FIG. 1B  is a representation of an example of the output of an R-C relaxation oscillator; 
       FIG. 2A  (prior art) is a simplified conceptual schematic diagram representative of a constant-current relaxation oscillator circuit known in the arts; 
       FIG. 2B  is a representation of an example of the output of a constant-current relaxation oscillator; 
       FIG. 3  (prior art) is a simplified schematic conceptual diagram representative of a band-gap voltage referenced relaxation oscillator circuit known in the arts; 
       FIG. 4  is a simplified schematic diagram of an example of a preferred embodiment of a relaxation oscillator according to the invention; 
       FIG. 5  is a simplified schematic diagram of an example of a preferred embodiment of a reference voltage generator for use in the preferred embodiment of the invention exemplified in  FIG. 4 ; 
       FIG. 6  is a graphical representation of the reference voltage over various temperatures and resistor values in the exemplary embodiment of the invention depicted in  FIG. 4 ; and 
       FIG. 7  is a graphical representation of an example of compensation for temperature variation in the exemplary embodiment of the invention depicted in  FIG. 4 . 
   

   References in the detailed description correspond to like references in the various drawings unless otherwise noted. Descriptive and directional terms used in the written description such as first, second, top, bottom, upper, side, etc., refer to the drawings themselves as laid out on the paper and not to physical limitations of the invention unless specifically noted. The drawings are not to scale, and some features of embodiments shown and discussed are simplified or amplified for illustrating the principles, features, and advantages of the invention. 
   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   The invention uses circuit techniques to limit relaxation oscillator output frequency variation to the absolute variation of hole mobility U p  in the process. Preferably, temperature variation of U p  is also cancelled out to a good extent. The methods and circuits described provide oscillator output with a tightly controlled frequency distribution. Referring primarily to  FIG. 4 , topology representative of a preferred embodiment of a relaxation oscillator circuit  10  according to the invention is shown. Those skilled in the arts will recognize that the present invention is not limited to a specific frequency range nor to a specific selection of transistors, logic elements, or other circuit components. The examples shown and described are representative of a particular preferred embodiment of the invention and it is anticipated that various circuitry may also be used to implement the invention. 
   In the preferred embodiment of the invention shown in  FIG. 4 , the relaxation oscillator  40  is implemented on a single monolithic integrated circuit. The precision relaxation oscillator  40  includes an oscillation generator  42 . Typically the oscillation generator  42  has two capacitors CA, CB, each coupled between an inverter INVA, INVB, and a comparator circuit  44 . The oscillation generator  42  operates by allowing one capacitor, for example CA, to charge while allowing the other capacitor, in this example CB, to discharge. The discharge path for each capacitor CA, CB, is coupled to the input of a respective comparator COMPA, COMPB of the comparator circuit  44 . A switch circuit  46 , in this example implemented using a series of NOR gates, is configured to alternately set and reset as the capacitors CA, CB alternately charge and discharge, thus producing a clock output VOUT. Although a constant-current relaxation oscillator topology  40  is shown and described in this example, it should be recognized that alternative topologies may also be used without departure from the invention. A reference voltage circuit  48  provides a reference voltage V REF  to the comparator circuit  44  for comparison to the voltage across each capacitor CA, CB. Various topologies of reference voltage circuits  48  may also be used so long as the reference voltage V REF  generator functions as described herein. 
   
     
       
         
           
             
               
                 I 
                 = 
                 
                   
                     Vbg 
                     / 
                     R 
                   
                   = 
                   
                     
                       C 
                       . 
                       
                         ⅆ 
                         V 
                       
                     
                     / 
                     
                       ⅆ 
                       t 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   14 
                 
                 ) 
               
             
           
           
             
               
                 
                   t 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
                 = 
                 
                   
                     t 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       C 
                       . 
                       VREF 
                     
                     / 
                     I 
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   15 
                 
                 ) 
               
             
           
           
             
               
                 f 
                 = 
                 
                   
                     1 
                     / 
                     
                       ( 
                       
                         
                           t 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         
                           t 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       Vbg 
                       / 
                       2. 
                     
                     ⁢ 
                     
                       C 
                       . 
                       R 
                       . 
                       VREF 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   16 
                 
                 ) 
               
             
           
         
       
     
   
   From equations 13 and 16, it can be seen that the frequency in the constant-current oscillator depends on the R-C product of the on-chip components. The variation from the resistor R is cancelled out according to the invention if the voltage reference V REF  for the comparator is made a function of the resistor value R. Specifically, if V REF  (or V b −V a  in equation 13) varies as 1/R, it will cancel out the variation of the resistor R. An example of the circuit topology of a reference voltage generator  48  used in the preferred embodiment of the invention illustrated in  FIG. 4 , is shown in more detail in  FIG. 5 . In this voltage reference generator circuit  48 , Resistors R 1  and R 20  are the same kind as the resistance R used to generate the current I BG  from the band-gap voltage V BG , and hence have the same variation. Hereinafter this parallel combination (R 1 , R 20 ) is denominated R p . Current mirrors MP 4 , MP 11 , MN 4 , MN 5 , MN 7  and MN 8  force the currents in the two paths  52 ,  54 , to be equal. MP 4  and MP 11  are sized differently, with MP 11  preferably being the larger. In the presently preferred embodiment, S 11  (W 11 /L 11 ) is 5/3 times larger than S 4 . The current I P  in either MP 11  or MP 4  is equal to (VGS mp4 −VGS mp11 )/(R P ). This current I P  is then mirrored by transistors MP 8 , MP 7 , MP 9 , and MP 5  and is used to generate the reference voltage V REF  with a 1/R P  dependency. The 1/R P  dependency occurs since the resistor R REF  (R 13 +R 21 ) is of the same kind as R P  and has the same process variation as R p . It can be shown that the current I P  has a 1/R P   2  dependency, as described by Equations 17-21. Typically, transistors MP 0 , MP 1 , MN 2 , MN 10  and MN 11  are used for start-up purposes and are not essential to the invention. 
   
     
       
         
           
             
               
                 Rp 
                 = 
                 
                   R 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                   ⁢ 
                   
                      
                   
                   ⁢ 
                   R 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   20 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   17 
                 
                 ) 
               
             
           
           
             
               
                 Ip 
                 = 
                 
                   
                     ( 
                     
                       
                         VGSmp 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         4 
                       
                       - 
                       
                         VGSmp 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         11 
                       
                     
                     ) 
                   
                   / 
                   Rp 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   18 
                 
                 ) 
               
             
           
           
             
               
                 Ip 
                 = 
                 
                   
                     { 
                     
                       
                         Sqrt 
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             
                               I 
                               / 
                               
                                 ( 
                                 
                                   
                                     Up 
                                     . 
                                     Cox 
                                     . 
                                     S 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   4 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                       - 
                       
                         Sqrt 
                         ⁡ 
                         
                           [ 
                           
                             2 
                             ⁢ 
                             
                               I 
                               / 
                               
                                 ( 
                                 
                                   
                                     Up 
                                     . 
                                     Cox 
                                     . 
                                     S 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                     } 
                   
                   / 
                   Rp 
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   19 
                 
                 ) 
               
             
           
           
             
               
                 Ip 
                 = 
                 
                   
                     { 
                     
                       2 
                       / 
                       
                         ( 
                         
                           
                             Up 
                             . 
                             Cox 
                             . 
                             S 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4. 
                           ⁢ 
                           
                             ( 
                             
                               Rp 
                               ^ 
                               2 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     } 
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           [ 
                           
                             1 
                             - 
                             
                               Sqrt 
                               ⁡ 
                               
                                 ( 
                                 
                                   S 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     4 
                                     / 
                                     S 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                         ^ 
                       
                       ⁢ 
                       2 
                     
                     } 
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   20 
                 
                 ) 
               
             
           
           
             
               
                 Vref 
                 = 
                 
                   
                     Ip 
                     . 
                     Rref 
                   
                   = 
                   
                     
                       { 
                       
                         2 
                         ⁢ 
                         
                           Rref 
                           / 
                           
                             ( 
                             
                               
                                 Up 
                                 . 
                                 Cox 
                                 . 
                                 S 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4. 
                               ⁢ 
                               
                                 ( 
                                 
                                   Rp 
                                   ^ 
                                   2 
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           [ 
                           
                             1 
                             - 
                             
                               Sqrt 
                               ⁡ 
                               
                                 ( 
                                 
                                   S 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     4 
                                     / 
                                     S 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                         ^ 
                         2 
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   21 
                 
                 ) 
               
             
           
         
       
     
   
   One potential source of frequency variation when using V REF  as a reference is that it depends on the hole mobility U p  in the materials used, which varies over temperature and process. In order to cancel out the temperature variation of U p , a current Proportional To Absolute Temperature (PTAT) is preferably used for charging the capacitors CA, CB shown in the example of  FIG. 4 . By adjusting the sizes of MP 11  and MP 4 , their size ratio may be fixed empirically such that the temperature constant (TC) of V REF  is approximately the same as the I PTAT  used as the current reference for the oscillator design. The 1/R P  dependency of V REF  over resistor variation and temperature variation are further illustrated in  FIG. 6  and  FIG. 7 . 
   The 1/R P  dependency of V REF  over resistor variation is illustrated in the example of  FIG. 6 . The variation of the reference voltage VREF is shown for traces indicating three temperature levels of −40 degrees, 27 degrees, and 150 degrees Celsius over a range of resistances. It can be seen that as the resistor value depicted along the x-axis is changes by a factor of two, the reference voltage correspondingly changes by a factor of approximately two. 
     FIG. 7  provides a graphic representation of the reference voltage VREF and VPTAT over a range of temperatures from −50 degrees to 150 degrees Celsius. It can be seen that the reference voltage V REF  roughly matches voltage (VPTAT) generated by placing a resistor across the reference current I PTAT . 
   Referring again to  FIG. 4  and the 1/R P  referenced oscillator design, the voltage V REF  that has a 1/R P  dependency is used to set the reference voltage VREF of the comparators COMPA, COMPB. An I PTAT  current is used to charge the capacitors CA, CB, and this current itself has a 1/R P  dependency since an on-chip resistor R is used to generate it from the band-gap voltage V BG . It should be noted with reference to Equation 21 that the reference voltage V REF  generated from the 1/R block also depends on Cox. If the timing capacitor in the oscillator design is also from the gate capacitance of a PMOS device, the variation in capacitor values can be cancelled out with the variation of VREF on Cox. This way both the R and C variation can be cancelled out and the frequency depends only upon the hole mobility U p  in the process. The temperature variation in the oscillator frequency, or a general time reference constructed out of monolithic components, can thus be made process insensitive except for a dependence on mobility. In order to cancel out the temperature variation of mobility, a temperature dependent current is preferably used as the charging current such that its temperature coefficient is the same as that of the mobility of holes, or electrons as the case may be. An approximation of such a temperature dependent current is a PTAT current. Using the I PTAT  current for charging the capacitors cancels out the temperature variation of U p . This makes the frequency of the oscillator remain constant even as process, temperature and supply variations occur except for variations in absolute value of U p . The cancellation process is more evident in the following equations where Equation 21 and Equation 16 are used to derive the frequency of the oscillator. 
   
     
       
         
           
             
               
                 
                   
                     Sc 
                     = 
                     
                       W 
                       × 
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       for 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       capacitor 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   C 
                   = 
                   
                     
                       Sc 
                       . 
                       Cox 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     if 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     PMOS 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gate 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     capacitance 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     is 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     used 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     set 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     timing 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     capacitor 
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   substituting 
                   ⁢ 
                   
                     
                         
                     
                     ⁢ 
                     
                         
                     
                   
                   ⁢ 
                   eq 
                   ⁢ 
                   
                     - 
                   
                   ⁢ 
                   21 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   in 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   eq 
                   ⁢ 
                   
                     - 
                   
                   ⁢ 
                   16 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   and 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   VPTAT 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   for 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     Vbg 
                     ⁡ 
                     
                       ( 
                       
                         since 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         current 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         is 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         now 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         PTAT 
                       
                       ) 
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   f 
                   = 
                   
                     
                       { 
                       
                         
                           VPTAT 
                           . 
                           Up 
                           . 
                           Cox 
                           . 
                           S 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         4. 
                         ⁢ 
                         
                           
                             ( 
                             
                               Rp 
                               ^ 
                               2 
                             
                             ) 
                           
                           / 
                           
                             ( 
                             
                               4. 
                               ⁢ 
                               
                                 Sc 
                                 . 
                                 Cox 
                                 . 
                                 R 
                                 . 
                                 Rref 
                               
                             
                             ) 
                           
                         
                       
                       } 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           [ 
                           
                             1 
                             - 
                             
                               Sqrt 
                               ⁡ 
                               
                                 ( 
                                 
                                   S 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     4 
                                     / 
                                     S 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                         ^ 
                         2 
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   22 
                 
                 ) 
               
             
           
           
             
               
                 
                   
                     Since 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     R 
                   
                   , 
                   
                     Rp 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Rref 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     have 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     same 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     variation 
                   
                   , 
                   
                     they 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cancel 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     out 
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   f 
                   = 
                   
                     
                       { 
                       
                         
                           VPTAT 
                           . 
                           Up 
                           . 
                           S 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           4 
                           / 
                           
                             ( 
                             
                               4. 
                               ⁢ 
                               Sc 
                             
                             ) 
                           
                         
                       
                       } 
                     
                     ⁢ 
                     
                       { 
                       
                         
                           [ 
                           
                             1 
                             - 
                             
                               Sqrt 
                               ⁡ 
                               
                                 ( 
                                 
                                   S 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     4 
                                     / 
                                     S 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                         ^ 
                         2 
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   eq 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   23 
                 
                 ) 
               
             
           
         
       
     
   
   From Equation 23, it can be seen that the only process variation that effects the frequency is variation in U p . The reduced frequency variation of the invention is further evident from the data in Table 2, which has the same corner variations as in Table 1. 
   
     
       
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
                 
                 
               Trim = 01 
               Trim = 01 
               Trim = 11 
             
             
               Supply 
                 
               NOMINAL 
               WEAK fre- 
               STRONG 
             
             
               Voltage 
               TEMP 
               Frequency (MHz) 
               quency (MHz) 
               Frequency (MHz) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               1.65 
               −40 
               5.22 
               4.90 
               5.56 
             
             
               1.65 
               27 
               5.08 
               4.84 
               5.32 
             
             
               1.65 
               150 
               4.87 
               4.82 
               4.95 
             
             
               1.80 
               −40 
               5.25 
               4.93 
               5.60 
             
             
               1.80 
               27 
               5.11 
               4.88 
               5.36 
             
             
               1.80 
               150 
               4.90 
               4.85 
               5.00 
             
             
               1.95 
               −40 
               5.28 
               4.95 
               5.63 
             
             
               1.95 
               27 
               5.14 
               4.90 
               5.39 
             
             
               1.95 
               150 
               4.93 
               4.88 
               5.00 
             
             
                 
             
           
        
       
     
   
   It may be seem by comparison of Table 2 with Table 1, that the frequency variation, previously 3.6 MHz in the absence of trim, has been reduced to 0.8 MHz with the maximum at 5.63 MHz and minimum at 4.82 MHz. The variation over temperature is also reduced considerably. 
   To summarize and reiterate the principles and practice of the invention, a process insensitive time reference can be created by using a charging capacitor and using a current to charge it. By creating a voltage reference that varies with resistor variation as 1/R, the variation of the charging current due to resistance variations can be compensated. In addition, the described voltage reference depends on the gate oxide of MOS devices (varies as 1/Cox), and this can be used to balance out the variation of the charging capacitor itself when the reference circuit is constructed using MOS gate capacitance. This voltage reference however, has a temperature variation as well. In order to cancel the variation due to temperature, the charging current is made to vary over temperature more or less as (1/Up) varies over temperature. This variation is approximated to a PTAT current variation in the oscillator circuit that is described here in detail. Those skilled in the arts will appreciate that the invention shown and described in the exemplary embodiment may be used in various other applications as well. Using the above techniques, it is possible to create accurate periodic waveforms as well as constant pulses of fixed duration that may be used for digital filtering applications, for example. The equations below summarize the cancellation techniques and provide an equation for the time reference dT. 
                   dT   =       C   .   dv     /   i       ⁢     
     ⁢     i   =     function   ⁢           ⁢     (     1   /   R     )         ⁢     
     ⁢     dv   =     function   ⁢           ⁢     (     1   /     R   .   Cox       )         ⁢     
     ⁢     dT   =       1   /   f     =       {       (     4.   ⁢     Sc   .   Cox   .   R   .   Rref       )     /     (       VPTAT   .   Up   .   Cox   .   S     ⁢           ⁢   4.   ⁢     (     Rp   ^   2     )       )       }     .     {     1   /       [     1   -     Sqrt   ⁡     (     S   ⁢           ⁢     4   /   S     ⁢           ⁢   11     )         ]     ^   2       }                   (     eq   ⁢           ⁢   24     )               
It will be understood by those skilled in the arts that when a selected circuit parameter is known, such as for example, a frequency desired for a particular application, the additional attributes of the circuit described by equation 24 may be chosen based on available materials, related circuitry, or other factors.
 
   The methods and devices of the invention provide advantages including but not limited to, in a preferred embodiment, providing improved relaxation oscillator frequency performance and the elimination of the need for external trimming. The invention provides superior time reference circuits and methods for their implementation. While the invention has been described with reference to certain illustrative embodiments, the methods and circuits described are not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments as well as other advantages and embodiments of the invention will be apparent to persons skilled in the art upon reference to the drawings, description, and claims.