10

SP8853A/B

Fig. 9 Standard form of second order loop filter

Fig. 10 Modified 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

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

t

…(1)

…(2)

2

z

where

N is the division ratio from VCO to reference frequency

z

is the damping factor = 0·7071

The SP8853 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 R

1

is feeding the virtual earth point of an operational amplifier

from a voltage source,

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

in V/radian which would produce the set current.

The digital phase detector used in the SP8853 is linear

over a range of 2

gain is given by:

Phase detector current setting

2

p

For

of 50

µA, the phase detector gain is therefore:

µA/radian

−

+

R1

C1

R2

R3

C2

FROM PHASE

DETECTOR

TO VCO

−

+

C1

R2

PHASE

DETECTOR

50

µA

2

p

3

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

for

= 0·00796V/radian

Example

Calculate values for a second order loop with the following

parameters:

Frequency to be synthesised

= 800MHz

Reference frequency

=100kHz

= 8000

Division ration

N

=

From equation (1),

t

800MHz

100kHz

From equation (2),

t

Now, since

t

230·7071

2p3500

∴C

and, since

t

∴R

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

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

for Fig. 11

and for Fig. 12

The equations are:

t

t

t

t

t

t

t

1

2

…(4)

2

t

…(5)

…(3)

t

11

2

2

11

3

2









1

2

1