In order to enlarge the hold-in range I modified the control filter and increased the gain by factor of 25 in the PLL.

It successfully enlarged the range, however the lock was easily broken by a small frequency change.

So I put a low frequency boost (LFB) and it successfully engaged the PLL stiffer.

Now it can maintain the lock even when the frequency disturbance of about 1MHz/s is applied.

(enlargement of the hold-in range)

I modified the control filter by replacing some resistors in the circuit to increase the gain by factor of 25.

        - R18 390 [Ohm]  => 200 [Ohm]

    - R20 1000 [Ohm] => 5000 [Ohm]

    - R41 39 [Ohm] => 10 [Ohm]

 This replacement also changes the location of the pole and the zero

    - pole 1.5 [Hz] => 0.3 [Hz]

    - zero 40 [Hz] => 159 [Hz]

 Note that this replacement doesn't so much change the UGF which was about 20 kHz before.

It becomes able to track the input frequency range of +/- 5MHz if I slowly changes the frequency of the input signal. 

However the PLL is not so strong enough to track ~ 1 kHz / 0.1s frequency step.  

(make the PLL stiffer : a low frequency boost)

One of the solution to make the PLL stiffer is to put a boost filter in the loop.

I used another channel to more drive the VCO at low frequency. See the figure below.

The 80MHz VCO box originally has two input channels, one of these inputs was usually disabled by MAX333A.

This time I activated both two input channels and put the input signal to each of them.

Before signals go to the box, one of the signal path is filtered by SR560. The filter has G=20000, pole=0.3Hz. So it gives a big low frequency boost.

Once the PLL was achieved without the boost, I increased the filter gain of SR560 to 20000 because locking with the boost is difficult as usual.