Nct controller reported assigning an air carrier an altitude to stay above unidentified VFR traffic....

Attributes
ACN	1350273
Time
Date	201604
Local Time Of Day	1801-2400
Place
Locale Reference	NCT.TRACON
State Reference	CA
Environment
Flight Conditions	VMC
Light	Night
Aircraft 1
Make Model Name	Large Transport Low Wing 2 Turbojet Eng
Operating Under FAR Part	Part 121
Flight Phase	Initial Approach
Route In Use	STAR EMZOH3
Flight Plan	IFR
Aircraft 2
Make Model Name	Small Aircraft
Operating Under FAR Part	Part 91
Flight Phase	Climb
Person 1
Function	Approach
Qualification	Air Traffic Control Fully Certified
Experience	Air Traffic Control Time Certified In Pos 1 (yrs) 0.8
Events
Anomaly	ATC Issue All Types Conflict Airborne Conflict

Narrative:

I issued aircraft X a clearance for the ILS approach. As aircraft X was descending on the EMZOH3 arrival I observed an unidentified VFR aircraft 12 miles west level at 4000 feet in the flight path of aircraft X. I cancelled aircraft X approach clearances and assigned 5500 feet to pass above the VFR traffic. The unidentified VFR aircraft proceeded to climb at a quick rate which then caused aircraft X to respond to an RA to descend.on this sector we are not protected by the class B which causes numerous VFR aircraft to transition through the finals of the airport. We can assume at times the path and altitude the unidentified VFR aircraft take; but usually it's difficult to plan on what action to take to avoid these aircraft. An extended class C or a lower class B may prove beneficial.

Original NASA ASRS Text

Title: NCT Controller reported assigning an air carrier an altitude to stay above unidentified VFR traffic. The VFR traffic climbed toward the air carrier which responded to a TCAS RA alert.

Narrative: I issued Aircraft X a clearance for the ILS approach. As Aircraft X was descending on the EMZOH3 Arrival I observed an unidentified VFR aircraft 12 miles west level at 4000 feet in the flight path of Aircraft X. I cancelled Aircraft X approach clearances and assigned 5500 feet to pass above the VFR traffic. The unidentified VFR aircraft proceeded to climb at a quick rate which then caused Aircraft X to respond to an RA to descend.On this sector we are not protected by the Class B which causes numerous VFR aircraft to transition through the finals of the airport. We can assume at times the path and altitude the unidentified VFR aircraft take; but usually it's difficult to plan on what action to take to avoid these aircraft. An extended Class C or a lower Class B may prove beneficial.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Nct controller reported assigning an air carrier an altitude to stay above unidentified VFR traffic. The VFR traffic climbed toward the air carrier which responded to a TCAS RA alert.