BC41B143A-DS-003PC Datasheet, PDF (52/94 Pages) List of Unclassifed Manufacturers – BlueCore 4-ROM Plug-n-Go Single Chip Bluetooth v2.0 + EDR System

Device Terminal Descriptions
10.3.4 Transconductance Driver Model
The crystal and its load capacitors should be viewed as a transimpedance element, whereby a current applied to one
terminal generates a voltage at the other. The transconductance amplifier in BlueCore4-ROM Plug-n-Go uses the
voltage at its input, XTAL_IN, to generate a current at its output, XTAL_OUT. Therefore, the circuit will oscillate if the
transconductance, transimpedance product is greater than unity. For sufficient oscillation amplitude, the product
should be greater than three. The transconductance required for oscillation is defined by the relationship shown in
Equation 10.5:
g_m
>
(2πF_X )²R_m((C₀
+
3(C_t1 + C_trim )(C_t2 + ) C_trim
C_int )(C_t1 + C_t2 + ) 2C_trim + (C_t1 +
C_{tr im} )(C_{t 2}
+
C_trim ))²
Equation 10.5: Transconductance Required for Oscillation
BlueCore4-ROM Plug-n-Go guarantees a transconductance value of at least 2mA/V at maximum drive level.
Notes:
More drive strength is required for higher frequency crystals, higher loss crystals (larger R_m) or higher capacitance
loading.
Optimum drive level is attained when the level at XTAL_IN is approximately 1V pk-pk. The drive level is
determined by the crystal driver transconductance, by setting the PS Key PSKEY_XTAL_LVL (0x241).
10.3.5 Negative Resistance Model
An alternative representation of the crystal and its load capacitors is a frequency dependent resistive element. The
driver amplifier may be considered as a circuit that provides negative resistance. For oscillation, the value of the
negative resistance must be greater than that of the crystal circuit equivalent resistance. Although the BlueCore4-ROM
Plug-n-Go crystal driver circuit is based on a transimpedance amplifier, an equivalent negative resistance may be
calculated for it with the following formula in Equation 10.6:
R_neg
>
g_m(2πF_X )²(C₀
3(C_t1 + C_trim)(C_t2 + ) C_trim
+ C_int )((C_t1 + C_t2 + ) 2C_trim + (C_t1 + C_trim)(C_t2
+ C_trim))²
Equation 10.6: Equivalent Negative Resistance
This formula shows the negative resistance of the BlueCore4-ROM Plug-n-Go driver as a function of its drive strength.
The value of the driver negative resistance may be easily measured by placing an additional resistance in series with
the crystal. The maximum value of this resistor (oscillation occurs) is the equivalent negative resistance of the
oscillator.
BC41B143A-ds-003Pc
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© Cambridge Silicon Radio Limited 2005
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