Twenty kilobytes is 163,840 bits. Divide that by the number of pixels and you get the average number of bits the encoder can spend on each pixel:
| Dimensions | Pixels | Bits available per pixel |
|---|---|---|
| 200 x 80 (signature) | 16,000 | 10.2 |
| 300 x 400 (small photo) | 120,000 | 1.37 |
| 600 x 600 | 360,000 | 0.46 |
| 1200 x 1200 | 1,440,000 | 0.11 |
The fewer bits each pixel gets, the more blocky and smeared a JPG looks. That is why a signature fits easily, a passport-size photo usually fits with acceptable quality, and a full phone photo has to be shrunk heavily.