awk: for loop output file name

In simple terms, there are file1.txt, file2.txt, file3.txt

file1.txt as follows:

1 a 4
d d g

file2.txt as follows:

2 b g
6 9 0

file3.txt as follows:

g h g
0 8 h

I now want the second column of the three files and their corresponding file name are printed out, and append to a file named all.txt

all.txt contents are as follows:

a file1.txt
d file1.txt
b file2.txt
9 file2.txt
h file3.txt
8 file3.txt

How to achieve the above demand it, here are two methods.

The first, is to add FILENAME way.

such as.

for i in *.txt
do
echo $i
awk ' print $2,FILENAME}' >> all.txt
done

Second. It is without FILENAME way.

for i in *.txt
do
echo $i
awk ' print $2,"'"${i}"'"}' >> all.txt
done