Quantized Sample Value Level SQNR* Quantized Sample Value Level SQNR* Quantized Sample Value Level SQNR* 6dB Volts**
Signed 16-bit Base 10 dBFS dB Signed 20-bit Base 10 dBFS dB Signed 24-bit Base 10 dBFS dB Steps Peak RMS
0111111111111111 +32767 0 96 01111111111111111111 +524287 0 120 011111111111111111111111 +8388607 0 144 0 1.414213562 1.000000000
0100000000000000 +16384 -6 90 01000000000000000000 +262144 -6 114 010000000000000000000000 +4194304 -6 138 1 0.707106781 0.500000000
0010000000000000 +8192 -12 84 00100000000000000000 +131072 -12 108 001000000000000000000000 +2097152 -12 132 2 0.353553391 0.250000000
0001000000000000 +4096 -18 78 00010000000000000000 +65536 -18 102 000100000000000000000000 +1048576 -18 126 3 0.176776695 0.125000000
0000100000000000 +2048 -24 72 00001000000000000000 +32768 -24 96 000010000000000000000000 +524288 -24 120 4 0.088388348 0.062500000
0000010000000000 +1024 -30 66 00000100000000000000 +16384 -30 90 000001000000000000000000 +262144 -30 114 5 0.044194174 0.031250000
0000001000000000 +512 -36 60 00000010000000000000 +8192 -36 84 000000100000000000000000 +131072 -36 108 6 0.022097087 0.015625000
0000000100000000 +256 -42 54 00000001000000000000 +4096 -42 78 000000010000000000000000 +65536 -42 102 7 0.011048543 0.007812500
0000000010000000 +128 -48 48 00000000100000000000 +2048 -48 72 000000001000000000000000 +32768 -48 96 8 0.005524272 0.003906250
0000000001000000 +64 -54 42 00000000010000000000 +1024 -54 66 000000000100000000000000 +16384 -54 90 9 0.002762136 0.001953125
0000000000100000 +32 -60 36 00000000001000000000 +512 -60 60 000000000010000000000000 +8192 -60 84 10 0.001381068 0.000976563
0000000000010000 +16 -66 30 00000000000100000000 +256 -66 54 000000000001000000000000 +4096 -66 78 11 0.000690534 0.000488281
0000000000001000 +8 -72 24 00000000000010000000 +128 -72 48 000000000000100000000000 +2048 -72 72 12 0.000345267 0.000244141
0000000000000100 +4 -78 18 00000000000001000000 +64 -78 42 000000000000010000000000 +1024 -78 66 13 0.000172633 0.000122070
0000000000000010 +2 -84 12 00000000000000100000 +32 -84 36 000000000000001000000000 +512 -84 60 14 0.000086317 0.000061035
0000000000000001 +1 -90 6 00000000000000010000 +16 -90 30 000000000000000100000000 +256 -90 54 15 0.000043158 0.000030518
0000000000000000 0 -∞ ε 00000000000000001000 +8 -96 24 000000000000000010000000 +128 -96 48 16 0.000021579 0.000015259
00000000000000000100 +4 -102 18 000000000000000001000000 +64 -102 42 17 0.000010790 0.000007629
00000000000000000010 +2 -108 12 000000000000000000100000 +32 -108 36 18 0.000005395 0.000003815
00000000000000000001 +1 -114 6 000000000000000000010000 +16 -114 30 19 0.000002697 0.000001907
00000000000000000000 0 -∞ ε 000000000000000000001000 +8 -120 24 20 0.000001349 0.000000954
000000000000000000000100 +4 -126 18 21 0.000000674 0.000000477
000000000000000000000010 +2 -132 12 22 0.000000337 0.000000238
000000000000000000000001 +1 -138 6 23 0.000000169 0.000000119
000000000000000000000000 0 -∞ ε 0.000000000 0.000000000
100000000000000000000001 -1 -138 6 23 -0.000000169 -0.000000119
100000000000000000000010 -2 -132 12 22 -0.000000337 -0.000000238
100000000000000000000100 -4 -126 18 21 -0.000000674 -0.000000477
100000000000000000001000 -8 -120 24 20 -0.000001349 -0.000000954
10000000000000000001 -1 -114 6 100000000000000000010000 -16 -114 30 19 -0.000002697 -0.000001907
10000000000000000010 -2 -108 12 100000000000000000100000 -32 -108 36 18 -0.000005395 -0.000003815
10000000000000000100 -4 -102 18 100000000000000001000000 -64 -102 42 17 -0.000010790 -0.000007629
10000000000000001000 -8 -96 24 100000000000000010000000 -128 -96 48 16 -0.000021579 -0.000015259
1000000000000001 -1 -90 6 10000000000000010000 -16 -90 30 100000000000000100000000 -256 -90 54 15 -0.000043158 -0.000030518
1000000000000010 -2 -84 12 10000000000000100000 -32 -84 36 100000000000001000000000 -512 -84 60 14 -0.000086317 -0.000061035
1000000000000100 -4 -78 18 10000000000001000000 -64 -78 42 100000000000010000000000 -1024 -78 66 13 -0.000172633 -0.000122070
1000000000001000 -8 -72 24 10000000000010000000 -128 -72 48 100000000000100000000000 -2048 -72 72 12 -0.000345267 -0.000244141
1000000000010000 -16 -66 30 10000000000100000000 -256 -66 54 100000000001000000000000 -4096 -66 78 11 -0.000690534 -0.000488281
1000000000100000 -32 -60 36 10000000001000000000 -512 -60 60 100000000010000000000000 -8192 -60 84 10 -0.001381068 -0.000976563
1000000001000000 -64 -54 42 10000000010000000000 -1024 -54 66 100000000100000000000000 -16384 -54 90 9 -0.002762136 -0.001953125
1000000010000000 -128 -48 48 10000000100000000000 -2048 -48 72 100000001000000000000000 -32768 -48 96 8 -0.005524272 -0.003906250
1000000100000000 -256 -42 54 10000001000000000000 -4096 -42 78 100000010000000000000000 -65536 -42 102 7 -0.011048543 -0.007812500
1000001000000000 -512 -36 60 10000010000000000000 -8192 -36 84 100000100000000000000000 -131072 -36 108 6 -0.022097087 -0.015625000
1000010000000000 -1024 -30 66 10000100000000000000 -16384 -30 90 100001000000000000000000 -262144 -30 114 5 -0.044194174 -0.031250000
1000100000000000 -2048 -24 72 10001000000000000000 -32768 -24 96 100010000000000000000000 -524288 -24 120 4 -0.088388348 -0.062500000
1001000000000000 -4096 -18 78 10010000000000000000 -65536 -18 102 100100000000000000000000 -1048576 -18 126 3 -0.176776695 -0.125000000
1010000000000000 -8192 -12 84 10100000000000000000 -131072 -12 108 101000000000000000000000 -2097152 -12 132 2 -0.353553391 -0.250000000
1100000000000000 -16384 -6 90 11000000000000000000 -262144 -6 114 110000000000000000000000 -4194304 -6 138 1 -0.707106781 -0.500000000
1000000000000000 -32768 0 96 10000000000000000000 -524288 0 120 100000000000000000000000 -8388608 0 144 0 -1.414213562 -1.000000000
* Signal to Quantization Noise Ratio ** Consumer Line Level 0dBV Reference 1.414213562 1.000000000
For each -6dB change, BOTH the positive phase AND the negative phase is reduced by one half (1/2).
Symmetrically. Not just one phase or the other. Changing only one phase or the other inflicts distortion and DC offset.
Notes: Formulas: Variables:
1) ∞ represents infinity. Level dBFS = 20Log(Qvalue/QvalueFS) QvalueFS is the full scale quantizied sample value.
2) ε represents infinitesimal. SQNR dB = 20Log(Qvalue/Qnoise) Qvalue is the quantized sample value.
3) dB is rounded to nearest integer. Qnoise is half the LSB value (0.5).