HD155121F Datasheet, PDF (55/57 Pages) Hitachi Semiconductor – RF Transceiver IC for GSM and PCN Dual band cellular systems

HD155121F
The open loop transfer function, Hol(S), of OPLL as shown in figure A-2 is given below.
Hol(S)
=
k _vr ⋅ k _dr ⋅ (S + ω_z )
C1⋅ C3 ⋅ R3 ⋅ S² ⋅ (S² + 2S ⋅ ω_p
+
ω_p2 )
=
k _vr ⋅ k _dr ⋅ (S + ω_z )
C1⋅ C3 ⋅ R3 ⋅ S² ⋅ (S + ω_p1) (S
+
ω_p2 )
ω_p =
C1+ C2 + C3
C1⋅ C2 ⋅ C3 ⋅ R2 ⋅ R3
ς = ^{ωp { C2 ⋅ R2 (C1+ C3) + C3 ⋅ R3(C1+ C2) }}
2 (C1+ C2 + C3)
ω_z
=
1
C2 ⋅ R2
ω_p1 = ω_p (ς − ς² − 1)
ω_p2 = ω_p (ς + ς² − 1)
Let:
C1 = 480 pF
C2 = 7.2 nF
C3 = 33 pF (VCO input capci tan ce on the control line)
R2 = 66 Ω
R3 = 804 Ω
Then:
ω_p = 35.70 × 10⁶ = 2π × 5.68 (MHz)
ς = 1.036
ω_z = 2.104 × 10⁶ = 2π × 335 (kHz)
ω_p1 = 27.32 × 10⁶ = 2π × 4.348 (MHz)
ω_p2 = 46.65 × 10⁶ = 2π × 7.425 (MHz)
k _vr = 2π × 30 × 10⁶ (rad / V sec)
k _dr = (1.7 × 10^−3 ) / π (A / rad)
The magnitude, | Hol(jω) |, and the phase, Φ(jω), of Hol(S) are as shown in the following equations. When
the above constants from ω_p to k_dr are substituted in the equations, then | Hol(jω) | and Φ(jω) in figure A-3
can be obtained.
Hol(jω) =
k _vr ⋅ k _dr ⋅
ω²
+
ω
2
p1
C1⋅ C3 ⋅ R3 ⋅ ω² ⋅
ω²
+
ω
2
p1
⋅
ω² + ω_p22
Φ(jω) = tan^−1 (ω / ω_z ) − tan^−1 (ω / ω_p1) − tan^−1 (ω / ω_p2 ) − 180 (deg)
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