AVR ADC clocking and sampling rate

1)ADC clockrate, sample per second(sps)

  ADC clock= xtal freq.(osc freq.)/division factor

 ADC Prescaler selection 

ADPS2	ADPS1	ADPS0	Division Factor
0	0	0	2
0	0	1	2
0	1	0	4
0	1	1	8
1	0	0	16
1	0	1	32
1	1	0	64
1	1	1	128

example:

 XATL =8Mhz,  division factor=128,    normal conversion = 13 cycles

 ADC clock = 8Mhz /128 = 62500hz = 62.5Khz ==>  T =16us

 sample per second(sps) = ADC clock/13 = 62500hz/13 = 4807.692hz  ==> T=208us

example:

ADC clock =  200 kHz , SPS=??

 sample per second(sps) = 200000/13 = 15384.615hz, around 15Khz

example:

ADC clock =  50 kHz , SPS=??

sample per second(sps) = 50000/13 = 3846.154,  around 3.8Khz

note:

     The successive approximation circuitry requires an input clock frequency between 50kHz and 200 kHz to achieve maximum resolution, 10 bits resolution.

     If a resolution of lower than 10 bits is required, the input clock frequency to the ADC can be higher than 200 kHz to achieve a higher sampling rate.  At 1MHz it is possible to achieve eight bits of resolution maximum.

example:
 XATL =8Mhz,  division factor=64(or 128),    normal conversion = 13 cycles

     ADC clock = 8Mhz /64 (or 128) = 125000hz (or 62500hz)

   sample per second(sps) = 125000hz (or 62500hz) /13 =9615 (or 4807) SPS

example:
 System Clock = 16Mhz, ADC Prescaler = 128, normal conversion = 13 cycles

     ADC Clk Freq = 125Khz  ==>T=8uS

    ADC conversion time = 104us (13 x ADC clk cycles)

   Maximum sample rate =sample per second(sps)=  1/104us = 9615 samples/second apprx

example:
 System Clock = 12.8MHz,  ADC Prescaler = 64,   normal conversion = 13 cycles

    ADC Clk Freq = 200Khz,   ==>T=5uS

   ADC conversion time = 65us (13 x ADC clk cycles)

   Maximum sample rate = 1/65us = 15385  samples/second apprx

example:
 System Clock = 8MHz,  ADC Prescaler = 32,   normal conversion = 13 cycles

     ADC Clk Freq = 8MHz/32=250Khz,   ==>T=4uS

   ADC conversion time = 52us (13 x ADC clk cycles)

   Maximum sample rate = 1/52us = 19230.77  samples/second apprx

example:
   Signal = 4 (or 4Khz or 400Khz or ....) 
   Sampling rate =  4 (or 4Khz or 400Khz or ....) 

example: Signal = 4 (or 4Khz or 400Khz or ....) 
              Sampling rate =  8 (or 8Khz or 800Khz or ....)  
            nyquist rule => Sampling rate = 2 X Signal freq.

example: Signal = 4 (or 4Khz or 400Khz or ....) 
              Sampling rate =  16 (or 16Khz or 1.6Mhz or ....)
              nyquist rule => Sampling rate = 4 X Signal freq.

example: Signal = 4 (or 4Khz or 400Khz or ....) 
              Sampling rate =  3.2 (or 3.2Khz or 320Khz or ....)
              under sampling  ==> Sampling rate = 4 /5 * Signal freq.

example: Signal = 9 (or 9Khz or 900Khz or ....) 
              Sampling rate =  4 (or 4Khz or 400Khz or ....) 
              under sampling  ==>Sampling rate = 4 /9 * Signal freq.