An eightbit digitalramp ADC with a 40mV resolution uses a cl

An eight-bit digital-ramp ADC with a 40-mV resolution uses a clock frequency of 2.5 MHz and a comparator with Vt = 1 mV. Determine the following values.

(a)* The digital output for VA = 6.000 V

(b) The digital output for 6.035 V

Knowing the number of bits of the Analog-to-Digital Converter (ADC), we can calculate the number of steps of the converter:

Steps = 2ⁿ

Steps = 2⁸ = 256 steps

Where, the maximum step would be:

MaxStep = 2ⁿ - 1

MaxStep = 2⁸ - 1 = 255

Using the resolution (40 mV) and the number of steps of the ADC, we can build a table to determine the maximum input voltage of the converter and every digital value equivalent to different analog inputs, just multiplying the resolution by the number of the step:

Vimax = 40mV x MaxStep

Vimax = 40mV x 255 = 10,2 V

Using this formula, we can build the following table:

At the table above, we see that the equivalent digital value for a 6 V analog input is 10010110 in binary and 150 in decimal.

The equivalent digital value for a 6,035 V analog input is the same as for a 6 V, since this value does not exceed the step value or resolution of 40 mV or 0,04 V. In a digital ramp ADC, the change in the analog input value must exceed the value of the resolution in order to change the digital output value.

The maximum conversion time is calculated for the maximum possible value of the analog input, which is 10,2 V. To convert this value to digital, the ADC needs 255 steps. The time of the steps is calculated inverting the frequency to obtain the period.

Tstep = 1 / f

Tstep = 1 / 2,5 MHz = 0,4 us

MaxT = 255 x 0,4 us = 102 us

The average time is the mean time between the fastest and slowest conversion

Fastest conversion time = 0 us

Slowest conversion time = 102 us

Average conversion time = 51 us

ANALOG INPUT	STEP	8-BITS DIGITAL OUTPUT
0 V	0	0	0	0	0	0	0	0	0
0,04 V	1	0	0	0	0	0	0	0	1
0,08 V	2	0	0	0	0	0	0	1	0
0,12 V	3	0	0	0	0	0	0	1	1
0,16 V	4	0	0	0	0	0	1	0	0
0,2 V	5	0	0	0	0	0	1	0	1
0,24 V	6	0	0	0	0	0	1	1	0
0,28 V	7	0	0	0	0	0	1	1	1
0,32 V	8	0	0	0	0	1	0	0	0
0,36 V	9	0	0	0	0	1	0	0	1
0,4 V	10	0	0	0	0	1	0	1	0
0,44 V	11	0	0	0	0	1	0	1	1
0,48 V	12	0	0	0	0	1	1	0	0
0,52 V	13	0	0	0	0	1	1	0	1
0,56 V	14	0	0	0	0	1	1	1	0
0,6 V	15	0	0	0	0	1	1	1	1
0,64 V	16	0	0	0	1	0	0	0	0
0,68 V	17	0	0	0	1	0	0	0	1
0,72 V	18	0	0	0	1	0	0	1	0
0,76 V	19	0	0	0	1	0	0	1	1
0,8 V	20	0	0	0	1	0	1	0	0
0,84 V	21	0	0	0	1	0	1	0	1
0,88 V	22	0	0	0	1	0	1	1	0
0,92 V	23	0	0	0	1	0	1	1	1
0,96 V	24	0	0	0	1	1	0	0	0
1 V	25	0	0	0	1	1	0	0	1
1,04 V	26	0	0	0	1	1	0	1	0
1,08 V	27	0	0	0	1	1	0	1	1
1,12 V	28	0	0	0	1	1	1	0	0
1,16 V	29	0	0	0	1	1	1	0	1
1,2 V	30	0	0	0	1	1	1	1	0
1,24 V	31	0	0	0	1	1	1	1	1
1,28 V	32	0	0	1	0	0	0	0	0
1,32 V	33	0	0	1	0	0	0	0	1
1,36 V	34	0	0	1	0	0	0	1	0
1,4 V	35	0	0	1	0	0	0	1	1
1,44 V	36	0	0	1	0	0	1	0	0
1,48 V	37	0	0	1	0	0	1	0	1
1,52 V	38	0	0	1	0	0	1	1	0
1,56 V	39	0	0	1	0	0	1	1	1
1,6 V	40	0	0	1	0	1	0	0	0
1,64 V	41	0	0	1	0	1	0	0	1
1,68 V	42	0	0	1	0	1	0	1	0
1,72 V	43	0	0	1	0	1	0	1	1
1,76 V	44	0	0	1	0	1	1	0	0
1,8 V	45	0	0	1	0	1	1	0	1
1,84 V	46	0	0	1	0	1	1	1	0
1,88 V	47	0	0	1	0	1	1	1	1
1,92 V	48	0	0	1	1	0	0	0	0
1,96 V	49	0	0	1	1	0	0	0	1
2 V	50	0	0	1	1	0	0	1	0
2,04 V	51	0	0	1	1	0	0	1	1
2,08 V	52	0	0	1	1	0	1	0	0
2,12 V	53	0	0	1	1	0	1	0	1
2,16 V	54	0	0	1	1	0	1	1	0
2,2 V	55	0	0	1	1	0	1	1	1
2,24 V	56	0	0	1	1	1	0	0	0
2,28 V	57	0	0	1	1	1	0	0	1
2,32 V	58	0	0	1	1	1	0	1	0
2,36 V	59	0	0	1	1	1	0	1	1
2,4 V	60	0	0	1	1	1	1	0	0
2,44 V	61	0	0	1	1	1	1	0	1
2,48 V	62	0	0	1	1	1	1	1	0
2,52 V	63	0	0	1	1	1	1	1	1
2,56 V	64	0	1	0	0	0	0	0	0
2,6 V	65	0	1	0	0	0	0	0	1
2,64 V	66	0	1	0	0	0	0	1	0
2,68 V	67	0	1	0	0	0	0	1	1
2,72 V	68	0	1	0	0	0	1	0	0
2,76 V	69	0	1	0	0	0	1	0	1
2,8 V	70	0	1	0	0	0	1	1	0
2,84 V	71	0	1	0	0	0	1	1	1
2,88 V	72	0	1	0	0	1	0	0	0
2,92 V	73	0	1	0	0	1	0	0	1
2,96 V	74	0	1	0	0	1	0	1	0
3 V	75	0	1	0	0	1	0	1	1
3,04 V	76	0	1	0	0	1	1	0	0
3,08 V	77	0	1	0	0	1	1	0	1
3,12 V	78	0	1	0	0	1	1	1	0
3,16 V	79	0	1	0	0	1	1	1	1
3,2 V	80	0	1	0	1	0	0	0	0
3,24 V	81	0	1	0	1	0	0	0	1
3,28 V	82	0	1	0	1	0	0	1	0
3,32 V	83	0	1	0	1	0	0	1	1
3,36 V	84	0	1	0	1	0	1	0	0
3,4 V	85	0	1	0	1	0	1	0	1
3,44 V	86	0	1	0	1	0	1	1	0
3,48 V	87	0	1	0	1	0	1	1	1
3,52 V	88	0	1	0	1	1	0	0	0
3,56 V	89	0	1	0	1	1	0	0	1
3,6 V	90	0	1	0	1	1	0	1	0
3,64 V	91	0	1	0	1	1	0	1	1
3,68 V	92	0	1	0	1	1	1	0	0
3,72 V	93	0	1	0	1	1	1	0	1
3,76 V	94	0	1	0	1	1	1	1	0
3,8 V	95	0	1	0	1	1	1	1	1
3,84 V	96	0	1	1	0	0	0	0	0
3,88 V	97	0	1	1	0	0	0	0	1
3,92 V	98	0	1	1	0	0	0	1	0
3,96 V	99	0	1	1	0	0	0	1	1
4 V	100	0	1	1	0	0	1	0	0
4,04 V	101	0	1	1	0	0	1	0	1
4,08 V	102	0	1	1	0	0	1	1	0
4,12 V	103	0	1	1	0	0	1	1	1
4,16 V	104	0	1	1	0	1	0	0	0
4,2 V	105	0	1	1	0	1	0	0	1
4,24 V	106	0	1	1	0	1	0	1	0
4,28 V	107	0	1	1	0	1	0	1	1
4,32 V	108	0	1	1	0	1	1	0	0
4,36 V	109	0	1	1	0	1	1	0	1
4,4 V	110	0	1	1	0	1	1	1	0
4,44 V	111	0	1	1	0	1	1	1	1
4,48 V	112	0	1	1	1	0	0	0	0
4,52 V	113	0	1	1	1	0	0	0	1
4,56 V	114	0	1	1	1	0	0	1	0
4,6 V	115	0	1	1	1	0	0	1	1
4,64 V	116	0	1	1	1	0	1	0	0
4,68 V	117	0	1	1	1	0	1	0	1
4,72 V	118	0	1	1	1	0	1	1	0
4,76 V	119	0	1	1	1	0	1	1	1
4,8 V	120	0	1	1	1	1	0	0	0
4,84 V	121	0	1	1	1	1	0	0	1
4,88 V	122	0	1	1	1	1	0	1	0
4,92 V	123	0	1	1	1	1	0	1	1
4,96 V	124	0	1	1	1	1	1	0	0
5 V	125	0	1	1	1	1	1	0	1
5,04 V	126	0	1	1	1	1	1	1	0
5,08 V	127	0	1	1	1	1	1	1	1
5,12 V	128	1	0	0	0	0	0	0	0
5,16 V	129	1	0	0	0	0	0	0	1
5,2 V	130	1	0	0	0	0	0	1	0
5,24 V	131	1	0	0	0	0	0	1	1
5,28 V	132	1	0	0	0	0	1	0	0
5,32 V	133	1	0	0	0	0	1	0	1
5,36 V	134	1	0	0	0	0	1	1	0
5,4 V	135	1	0	0	0	0	1	1	1
5,44 V	136	1	0	0	0	1	0	0	0
5,48 V	137	1	0	0	0	1	0	0	1
5,52 V	138	1	0	0	0	1	0	1	0
5,56 V	139	1	0	0	0	1	0	1	1
5,6 V	140	1	0	0	0	1	1	0	0
5,64 V	141	1	0	0	0	1	1	0	1
5,68 V	142	1	0	0	0	1	1	1	0
5,72 V	143	1	0	0	0	1	1	1	1
5,76 V	144	1	0	0	1	0	0	0	0
5,8 V	145	1	0	0	1	0	0	0	1
5,84 V	146	1	0	0	1	0	0	1	0
5,88 V	147	1	0	0	1	0	0	1	1
5,92 V	148	1	0	0	1	0	1	0	0
5,96 V	149	1	0	0	1	0	1	0	1
6 V	150	1	0	0	1	0	1	1	0
6,04 V	151	1	0	0	1	0	1	1	1
6,08 V	152	1	0	0	1	1	0	0	0
6,12 V	153	1	0	0	1	1	0	0	1
6,16 V	154	1	0	0	1	1	0	1	0
6,2 V	155	1	0	0	1	1	0	1	1
6,24 V	156	1	0	0	1	1	1	0	0
6,28 V	157	1	0	0	1	1	1	0	1
6,32 V	158	1	0	0	1	1	1	1	0
6,36 V	159	1	0	0	1	1	1	1	1
6,4 V	160	1	0	1	0	0	0	0	0
6,44 V	161	1	0	1	0	0	0	0	1
6,48 V	162	1	0	1	0	0	0	1	0
6,52 V	163	1	0	1	0	0	0	1	1
6,56 V	164	1	0	1	0	0	1	0	0
6,6 V	165	1	0	1	0	0	1	0	1
6,64 V	166	1	0	1	0	0	1	1	0
6,68 V	167	1	0	1	0	0	1	1	1
6,72 V	168	1	0	1	0	1	0	0	0
6,76 V	169	1	0	1	0	1	0	0	1
6,8 V	170	1	0	1	0	1	0	1	0
6,84 V	171	1	0	1	0	1	0	1	1
6,88 V	172	1	0	1	0	1	1	0	0
6,92 V	173	1	0	1	0	1	1	0	1
6,96 V	174	1	0	1	0	1	1	1	0
7 V	175	1	0	1	0	1	1	1	1
7,04 V	176	1	0	1	1	0	0	0	0
7,08 V	177	1	0	1	1	0	0	0	1
7,12 V	178	1	0	1	1	0	0	1	0
7,16 V	179	1	0	1	1	0	0	1	1
7,2 V	180	1	0	1	1	0	1	0	0
7,24 V	181	1	0	1	1	0	1	0	1
7,28 V	182	1	0	1	1	0	1	1	0
7,32 V	183	1	0	1	1	0	1	1	1
7,36 V	184	1	0	1	1	1	0	0	0
7,4 V	185	1	0	1	1	1	0	0	1
7,44 V	186	1	0	1	1	1	0	1	0
7,48 V	187	1	0	1	1	1	0	1	1
7,52 V	188	1	0	1	1	1	1	0	0
7,56 V	189	1	0	1	1	1	1	0	1
7,6 V	190	1	0	1	1	1	1	1	0
7,64 V	191	1	0	1	1	1	1	1	1
7,68 V	192	1	1	0	0	0	0	0	0
7,72 V	193	1	1	0	0	0	0	0	1
7,76 V	194	1	1	0	0	0	0	1	0
7,8 V	195	1	1	0	0	0	0	1	1
7,84 V	196	1	1	0	0	0	1	0	0
7,88 V	197	1	1	0	0	0	1	0	1
7,92 V	198	1	1	0	0	0	1	1	0
7,96 V	199	1	1	0	0	0	1	1	1
8 V	200	1	1	0	0	1	0	0	0
8,04 V	201	1	1	0	0	1	0	0	1
8,08 V	202	1	1	0	0	1	0	1	0
8,12 V	203	1	1	0	0	1	0	1	1
8,16 V	204	1	1	0	0	1	1	0	0
8,2 V	205	1	1	0	0	1	1	0	1
8,24 V	206	1	1	0	0	1	1	1	0
8,28 V	207	1	1	0	0	1	1	1	1
8,32 V	208	1	1	0	1	0	0	0	0
8,36 V	209	1	1	0	1	0	0	0	1
8,4 V	210	1	1	0	1	0	0	1	0
8,44 V	211	1	1	0	1	0	0	1	1
8,48 V	212	1	1	0	1	0	1	0	0
8,52 V	213	1	1	0	1	0	1	0	1
8,56 V	214	1	1	0	1	0	1	1	0
8,6 V	215	1	1	0	1	0	1	1	1
8,64 V	216	1	1	0	1	1	0	0	0
8,68 V	217	1	1	0	1	1	0	0	1
8,72 V	218	1	1	0	1	1	0	1	0
8,76 V	219	1	1	0	1	1	0	1	1
8,8 V	220	1	1	0	1	1	1	0	0
8,84 V	221	1	1	0	1	1	1	0	1
8,88 V	222	1	1	0	1	1	1	1	0
8,92 V	223	1	1	0	1	1	1	1	1
8,96 V	224	1	1	1	0	0	0	0	0
9 V	225	1	1	1	0	0	0	0	1
9,04 V	226	1	1	1	0	0	0	1	0
9,08 V	227	1	1	1	0	0	0	1	1
9,12 V	228	1	1	1	0	0	1	0	0
9,16 V	229	1	1	1	0	0	1	0	1
9,2 V	230	1	1	1	0	0	1	1	0
9,24 V	231	1	1	1	0	0	1	1	1
9,28 V	232	1	1	1	0	1	0	0	0
9,32 V	233	1	1	1	0	1	0	0	1
9,36 V	234	1	1	1	0	1	0	1	0
9,4 V	235	1	1	1	0	1	0	1	1
9,44 V	236	1	1	1	0	1	1	0	0
9,48 V	237	1	1	1	0	1	1	0	1
9,52 V	238	1	1	1	0	1	1	1	0
9,56 V	239	1	1	1	0	1	1	1	1
9,6 V	240	1	1	1	1	0	0	0	0
9,64 V	241	1	1	1	1	0	0	0	1
9,68 V	242	1	1	1	1	0	0	1	0
9,72 V	243	1	1	1	1	0	0	1	1
9,76 V	244	1	1	1	1	0	1	0	0
9,8 V	245	1	1	1	1	0	1	0	1
9,84 V	246	1	1	1	1	0	1	1	0
9,88 V	247	1	1	1	1	0	1	1	1
9,92 V	248	1	1	1	1	1	0	0	0
9,96 V	249	1	1	1	1	1	0	0	1
10 V	250	1	1	1	1	1	0	1	0
10,04 V	251	1	1	1	1	1	0	1	1
10,08 V	252	1	1	1	1	1	1	0	0
10,12 V	253	1	1	1	1	1	1	0	1
10,16 V	254	1	1	1	1	1	1	1	0
10,2 V	255	1	1	1	1	1	1	1	1

An eightbit digitalramp ADC with a 40mV resolution uses a cl

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