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Número de pieza

componentes Descripción

Fabricante

SP8861

1·3GHz Low Power Single-Chip Frequency Synthesiser

Mitel Networks 

SP8861

FROM PHASE

DETECTOR

C1 R2

R1

−

+

R3

TO VCO

C2

PHASE

DETECTOR

C1 R2

−

+

Fig. 9 Standard form of second order loop filter

LOOP CALCULATIONS

Many frequency synthesiser designs use a second order

loop with a loop filter of the form shown in Fig. 9.

In practice, an additional RC time constant (shown dashed

in Fig. 9) is often added to reduce noise from the amplifier. In

addition, any feedthrough capacitor or local decoupling at the

VCO will be added to the value of C2. These additional

components in fact form a third order loop and, if the values

are chosen correctly, the additional filtering provided can

considerably reduce the level of reference frequency sidebands

and noise without adversely affecting the loop settling time.

The calculations of values for both types of loop are shown

below.

Second Order Loop

For this filter, two equations are required to determine the

time constants t1 (= C1R1) and t2 (= C1R2); the equations are:

t1

=

KuK0

vn2N

…(1)

where

t2 =

2z

vn

…(2)

Ku is the phase detector gain factor in V/radian

K0 is the VCO gain factor = 2p310MHz/V

N is the division ratio from VCO to reference frequency

vn is the natural loop frequency = 500Hz

z is the damping factor = 0·7071

The SP8861 phase detector is a current source rather than

a conventional voltage source and has a gain factor specified

in µA/radian. Since the equations deal with a filter where R1

is feeding the virtual earth point of an operational amplifier

from a voltage source, R1 sets the input current to the filter –

similar to the circuit shown in Fig. 10 – where a current source

phase detector is connected directly to the virtual earth point

of the operational amplifier.

The equivalent voltage gain of the phase detector can be

calculated by assuming a value for R1 and calculating a gain

in V/radian which would produce the set current.

The digital phase detector used in the SP8861 is linear

over a range of 2p radians and therefore the phase detector

gain is given by:

Phase detector current setting

Ku =

2p

µA/radian

For R1 = 1kΩ and assuming a value of phase detector current

of 50µA, the phase detector gain is therefore:

Ku

=

50µA

2p

3103

= 0·00796V/radian

This value can now be inserted in equation 1 to obtain a value

for C1 and equation 2 used to determine a value for R2.

10

Fig. 10 Modified form of second order loop filter

Example

Calculate values for a second order loop with the following

parameters:

Frequency to be synthesised

= 800MHz

Reference frequency

=100kHz

Division ration N

=

800MHz

100kHz

= 8000

From equation (1),

t1 =(20p·037590603)223p83311006 3

∴t1 = 6·334µs

From equation (2),

t2

=

230·7071

2p3500

∴t2 = 450µs

Now, since t1 = C1R1 ,

C1

= 6·33431026

103

∴C1 = 6·33nF

and, since t2 = C1R2 ,

R2

=

4·531024

6·3331029

∴R2 = 71kΩ

Third Order Loop

The third order loop is normally as shown in Fig. 11. Fig. 12

shows the circuit redrawn to use an RC time constant after the

amplifier, allowing any feedthrough capacitance on the VCO

line to be included in the loop calculations. Where the modified

form in Fig. 12 is used, it is advantageous to connect a small

capacitor CX of typically 100pF (shown dashed) across R2 to

reduce sidebands caused by the amplifier being forced into

non-linear operation by the phase comparator pulses

Three equations are required to determine the time

constants t1, t2, and t3, where

for Fig. 11

and for Fig. 12

t1 = C1R1

t2 = R2 (C11C2)

t3 = C2R2

t1 = C1R1

t2 = C1R2

t3 = C2R3

The equations are:

t1 =

KuK0

vn2N

11vn2

t22



1

2

11vn2 t32 

…(3)

t2 =

1

vn2t32

t3

=

2tan

F0 1cos1F0

vn

…(4)

…(5)

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