From pressure to SPL : microphone calibration using sound level meter calibrator and sound level meter I have a microphone + signal conditioner with adjustable gain and filter. I capture amplified signal using oscilloscope. I'm using this signal to compute equivalent continuous sound level

With signal conditioner, I set needed gain and A-weighted filter.
From oscilloscope signal V I can get pressure p = V/ (gain x mic sensitivity)

We can suppose A-weighted filter filters out frequency out of audio range. So I can easily compute leq = 20 log10(rms(pa)/pref), pa is time domain pressure A filtered, pref is reference pressure = 20e-6 pa

I used a sound level calibrator to check if it works. I get a leq of ~94dB and 114dB when applying 94dB and 114dB level with calibrator. 

I also have a sound level meter, I also checked it with sound level calibrator. 
Now, in my room (some noise because of oscilloscope...) with A filter it measures ~46 dB(A). Now I put my microphone close to it, with microphone I get a leq of 55 dB. When changing sound level meter filter from A to C results are better : sound level meter measures ~56dB.
I changed microphone acquisition duration but leq results are same. 


How can we explain such leq difference when sound level meter and
microphone measure dB(A)?  
How can I calibrate my microphone with    sound level meter?
First, I would check the positioning of sound level meter and microphone. If you are putting them close to the oscilloscope a few centimeters of displacement may change the measured value dramatically. (6dB/doubling of distance)

Second, which microphone do you use? The link you provided leads to a preamplifier. The actual capsule can either be a free field or a pressure field one. A free field capsule should be facing the sound source directly, while a pressure field capsule should face it sideways.