CSP1027 Datasheet, PDF (44/64 Pages) Agere Systems – CSP1027 Voice Band Codec for Cellular Handset and Modem Applications

CSP1027 Voice Band Codec for
Cellular Handset and Modem Applications
Data Sheet
December 1999
7 Application Information (continued)
This change in frequency as function of load capacitance is known as pullability and is expressed in units of ppm/
pF. For small deviations of a few pF, pullability can be determined by the equation below.
pullability (ppm/pF) = ---⁽---^C----¹---⁾--⁽---¹---⁰----⁶---⁾---
2(C0 + CL)²
where
C0 = parasitic capacitance of crystal.
C1 = motional capacitance of crystal (usually around 1 fF—25 fF, value can be obtained from
crystal vendor).
CL = total load capacitance seen by crystal.
Note that for a given crystal, the pullability can be reduced, and hence, the frequency stability improved, by making
CL as large as possible while still maintaining sufficient negative resistance to ensure start-up per the curves
shown in Figures 31 and 32 on page 39.
Since it is not possible to know the exact values of the parasitic capacitance in a crystal-based oscillator system,
the external capacitors are usually selected empirically to null out the frequency offset on a typical prototype board.
Thus, if a crystal is specified to operate with a load capacitance of 10 pF, the external capacitors would have to be
made slightly less than 20 pF each in order to account for strays. Suppose, for instance, that a crystal for which
CL = 10 pF is specified is plugged into the system and it is determined empirically that the best frequency accuracy
occurs with CEXT = 18 pF. This would mean that the equivalent board and device strays from each lead to ground
would be 2 pF.
As an example, suppose it is desired to design a 26 MHz, 3.3 V system with ±100 ppm frequency accuracy. The
parameters for a typical high-accuracy, custom, 26 MHz fundamental mode crystal are as follows:
Initial Tolerance
Temperature Tolerance
Aging Tolerance
Series Resistance
Motional Capacitance (C1)
Parasitic Capacitance (C0)
10 ppm
25 ppm
6 ppm
20 Ω max
15 pF max
7 pF max
In order to ensure oscillator start-up, the negative resistance of the oscillator with load and parasitic capacitance
must be at least twice the series resistance of the crystal, or 40 Ω. Interpolating from Figure 32 on page 39, exter-
nal capacitors plus strays can be made as large as 30 pF while still achieving 40 Ω of negative resistance. Assume
for this example that external capacitors are chosen so that the total load capacitance including strays is 30 pF per
lead, or 15 pF total. Thus, a load capacitance, CL = 15 pF would be specified to the crystal manufacturer.
From the above equation, the pullability would be calculated as follows:
pullability = ---⁽---^C----¹---⁾--⁽---¹---⁰----⁶---⁾--- = ⁽---⁰---^.--⁰---¹----⁵---⁾---⁽--¹---⁰----⁶---⁾- = 15.5 ppm/pF
2(C0 + CL)² 2(7 + 15)²
If 2% external capacitors are used, the frequency deviation due to this variation is equal to
(0.02)(15 pF)(15.5 ppm/pF) = 4.7 ppm.
Note: To simplify analysis, CEXT is considered to be 30 pF. In practice, it would be slightly less than this value to
account for strays. Also, temperature and aging tolerance on the capacitors have been neglected.
Typical capacitance variation of oscillator circuit in the CSP1027 itself across process, temperature, and supply
voltage is ±1 pF. Thus, the expected frequency variation due to the CSP1027 is as follows:
(1 pF)(15.5 ppm/pF) = 15.5 ppm.
Approximate variation in parasitic capacitance of crystal = ±0.5 pF.
Frequency shift due to variation in C0 = (0.5 pF)(15.5 ppm/pF) = 7.75 ppm.
Approximate variation in parasitic capacitance of printed-circuit board = ±1.5 pF.
Frequency shift due to variation in board capacitance = (1.5 pF)(15.5 ppm/pF) = 23.25 ppm.
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