RPM drop during down/up shifting with AC on

[aliasim.asim]

I own 2010 Honda City 1.3 manual with 82,000 kms on odometer. When driving without AC the car runs smooth and accelerates fine, but with AC on I face two problems.
1. The car struggles a lot during acceleration
2. This is the most important point, with AC on whenever I down shift or up shift, after I release the clutch the RPM drops significantly and it feels like car is going to stall but within a second the RPM stables again and the everything is fine.
Is it a bad compressor? Does the compressor or pulley bearing need lubrication?
Again, if the AC is off and only the blower is on the car does the same thing but this time RPM drop is insignificant but I feel the blower is slowing down like it is not getting enough current. This makes me think that there might be something wrong with the alternator or battery...
Plz suggest how to diagnose this issue.

[israrmuaziz]

If its juddering when u let go of the throttle and comes back up. Start with the basics. When was the airfilter last changed? If it was changed recently then open op the air box and check if it’s blocked. Check the spark plugs and the fuel filter in the tank.

[omersiddiqui5482]

The Car needs to be tuned up. IAC and PCV should be checked. Clean up the throttle body. The ECU in the which is the cars computer should be increasing the RPM when the AC is turned on. There can also be a vacuum leak