Analog To Digital Converter | How ADC Works With PIC MCU

 

Analog To Digital Converter | How ADC Works And Reading Analog Signals

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	Embedded Systems Tutorials With PIC MCUs
	Intermediate Level ★★☆☆☆

 

In this tutorial, you’ll get a solid introduction to the analog signal conversion to the digital domain. And why it’s important to do so. And how does ADC work in order to achieve such a goal? And what are the fundamental limitations and challenges for practical ADC? We’ll also see different schemes for how to read an ADC with an 8-Bit Microcontroller from Microchip (PIC). By the end of this long tutorial, you’ll understand the fundamental foundations of ADC and you’ll also create the 2 projects below from scratch. And have your own device driver for ADC for any future project you wanna create. Stick with me it’s gonna be so long, hopefully, informative journey! And let’s get started!

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   Required Components   

Qty.	Component Name	Buy On Amazon.com
1	PIC16F877A	Add
1	BreadBoard	Add
1	Potentiometer	Add    Add
1	LED	Add    Add
1	Microphone	Add    Add
1	BC337 NPN BJT Transistor	Add    Add
1	Resistors Kit (to build audio amp.)	Add    Add
1	Capacitors Kit (to build audio amp.)	Add    Add
1	USB-TTL (FTDI) Serial Converter	Add
1	Jumper Wires Pack	Add    Add
1	LM7805 Voltage Regulator (5v)	Add
1	Crystal Oscillator	Add
1	PICkit2 or 3 Programmer	Add

The Prototyping Board Setup

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   What is Analog To Digital Conversion?   

It’s a process of capturing the analog electric signal (such as sound captured by a microphone) and converting it to a series of numeric “Digital” values to be stored/processed by a digital computer or DSP. The electronic device which is used for this conversion process has been known to be the A/D or ADC (Analog-To-Digital Converter).

There are many different types of A/D converters out there. And depending on how it works and how well it gets the job done, you pay more or less respectively per ADC unit.

And before any further investigation for ADC types and technical details of working principles, let us question about the usefulness of A/D conversion. Why do we need to use ADC in the first place?

 

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   Why We Need Analog To Digital Converters?   

 

Our need to convert analog signals to digital data stems from the fact that our computers are digital ones. They just can’t handle the analog signal and therefore, there should be a device which converts the signal from analog to digital domain (ADC).

Most signals are analog in nature and the electronic sensors which we’re using for capturing these phenomena are also analog. For example, the temperature sensor converts temperature in °C to an analog voltage that’s proportional to the value of temperature. So do the microphone, pressure sensor, light sensor and so on.

Hence, we need a way to read analog voltage and convert it to digital values which we can program our computers to manipulate it mathematically in order to achieve real-time monitoring and/or control or whatever.

 

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   How ADC Works?   

 

 General Block Diagram For ADC 

The basic structure of an ADC consists of an S/H circuit (Sample & Hold). Followed by a quantized which is actually the working horse for the analog to the digital conversion process. The type of ADC depends on how it’s performing the quantization process, it can be analog integration, digital counter, successive approximation, or even direct conversion as in Flash ADC types which we’ll discuss hereafter.

Finally, the digital output data is served to the CPU or gets directly stored in memory. The ADC can either be integrated within the MCU chip itself or a standalone IC that you can interface with Serial/Parallel ports of your microcontroller.

 Analog Reference For ADC 

Analog To Digital Conversion process needs an extremely stable voltage reference V_ref+ and V_ref– representing the maximum allowable voltage swing for the input in order to be correctly converted to digital value with respect to the limits which are set by the analog reference V_ref.

The easiest way to guarantee a stable V_ref is to use a resistor and a capacitor to resist any sudden drop in voltage and protect your system. You can also use a Zener diode as well to guarantee a stable voltage reference which immunes your system against any sudden changes in power supply increase/drop. The concept is indicated in the diagram below.

 ADC Sampling 

The Analog input signal which is a continuous function in time has to be held constant for a short period of time during which the ADC can convert the instantaneous value to its digital representation. This process is done by the Sample/Hold circuitry which is basically an Analog Switch + a Holding Capacitor. It can get more complicated in advanced converters but we’re assuming the very basic S/H circuitry.

Sampling Rate

The rate at which an ADC converts the continuous analog signal to digital data is called “Sampling Rate”. And if it takes Ts time to convert a single sample, then the sampling rate of this ADC is Fs = 1/Ts. Then the original analog signal can be reproduced from the discrete-time digital values by mathematical interpolation. The accuracy in this procedure is dictated by the combined effect of the sampling rate and quantization error.

Sampling Theorem

Theoretically, and to get the minimal information about the original analog signal, an ADC must sample and convert the analog signal with a frequency of Fs >= 2F_MAX Which satisfies the Shannon-Nyquist sampling theorem.

Fs -> The Sampling Frequency of an ADC

F_MAX -> The Maximum Frequency In The Analog Signal Being Converted

Violating this rule will lead to further problems and loss of significant information about the signal. It’s near to impossible to get an idea of what does the original signal look like before conversion. That’s why we practically pick an ADC with a sampling rate (Fs) of about 10 x F_MAX To avoid operating near to the fundamental limitations of the sampling.

Over-Sampling

Analog signals are usually sampled at the minimum allowable frequency for economical reasons. However, if an analog signal is sampled at a much higher rate than the Nyquist limitation and then got filtered by a digital filter to limit its bandwidth, we’ll have many interesting results “Achievements in fact”. For example, a 20-bit ADC can be made to act as a 24-bit ADC with 256× oversampling.

The over-sampling technique is typically used in audio frequency ADCs where the required sampling rate (typically 44.1kHz) is very low compared to the clock speed of typical logic circuits (>1MHz). In this case, by using the extra bandwidth to distribute quantization error onto out of band frequencies, the accuracy of the ADC can be greatly increased at no additional cost.

 ADC Resolution & Quantization 

Resolution

The Resolution of an ADC indicates the number of discrete values it can produce over the range of analog values. The Resolution also determines the magnitude of the quantization error and therefore determines the maximum possible average signal-to-noise ratio (SNR) for a typical ADC.

The resolution Q depends on both the number of bits n generated by the quantizer and also the FSR (full-scale range) for the analog reference voltage line. Here is the formula to calculate the resolution of quantization Q which is basically a division for the FSR voltage by the number of levels 2ⁿ

Which means, an 8-Bit ADC with an analog reference V_ref+of 5v has a resolution of

That’s why you can potentially increase the ADC conversion resolution by decreasing the analog voltage reference provided that you’re measuring small signals. Alternatively, you can amplify small signals like audio sound captured by a microphone which is typically in milli-volts range.

Quantization

The quantizer circuit is the working horse of an ADC. Its function is to convert the analog voltage captured by the S/H circuitry to the digital corresponding value. There are many schemes for creating a quantization circuit which also determines the type of an ADC. What you should really know in the meantime, that the quantization process whether it’s rounding-off or truncating intermediate analog signals which lie between two Q levels.

Quantization Error

The quantization error is due to the fact that analog signals will always lie between two distinct Q levels. Should we round-off or truncate? doing either will generate what we call “The Quantization Error”. And it can’t be avoided, However, we can improve the overall accuracy using different techniques.

The Signal To Quantization Noise Ratio (SQNR) is calculated using the following formula

There are many different schemes used by different types of ADCs for analog signal quantization. Hence, we have a variety of ADC types which we’ll be discussing hereafter. Most of which use analog comparators alongside a digital counter, analog integrator, or a D/A in order to achieve the Analog To Digital conversion.

 

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   Different Types of ADC   

 

There are many types for Analog To Digital Converters depending on the way they work. Here I’ll list some of the most commonly used ones whether for standalone ADC ICs or being integrated within microcontrollers. You can definitely research for whichever seems interesting to you as this is not going to be a heavily detailed demonstration.

 Counter Type ADC 

This type of ADC utilizes a DAC (Digital To Analog Converter) in order to perform a quick sweep for the output voltage up to the point where the analog comparator confirms that the output voltage is nearly equal to the analog input signal being measured. Therefore, the counter stops sweeping and its current value is the direct digital representation for the input signal.

The block diagram down below indicates how a Counter Type ADC works 

 Integrating (Dual-Slope) ADC 

An integrating ADC (dual-slope ADC) applies the analog input voltage to the input of an integrator and allows the voltage to ramp for a fixed time period (the run-up period). Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero (the run-down period).

The input voltage is computed as a function of the reference voltage, the constant run-up time period, and the measured run-down time period. The run-down time measurement is usually made in units of the converter’s clock, so longer integration times allow for higher resolutions.

The block diagram indicating the functionality of Dual-Slope (Integrating) ADC is shown below.

 Successive Approximation 

The Successive Approximation ADC uses a comparator to successively narrow a range that contains the analog input voltage. At each successive step, the converter compares the input voltage to the output of an internal DAC which might represent the midpoint of a selected voltage range. At each step in this process, the approximation is stored in the successive approximation register (SAR).

The block diagram indicating the functionality of Successive Approximation ADC is shown below.

 Flash Type ADC (Direct) 

The Flash type ADC consists of (2ⁿ-1) parallel analog comparators. These comparators are sampling the analog input signal in parallel and driving the logic circuit which generates the digital code for each voltage level. It’s also called direct conversion as it’s the fastest type of ADC at all.

However, it’s limited in resolution. Typically 8-Bits are being used commonly, as increasing the resolution by a single 1 bit will require twice the number of comparators being used. And therefore, it’s extremely expensive and has a large size.

The block diagram indicating the functionality of Flash Type ADC (3-Bit) is shown below.

 

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   ADC Module in PIC Microcontroller   

For the rest of this tutorial, we’ll discuss the ADC Module in PIC16F microcontrollers. How it works and how to configure and use it to read analog channels for our projects.

 Hardware Description 

The Analog-to-Digital (A/D) Converter module has 5-Channels for the 28-pin devices and 8-Channels for the 40/44-pin devices. The conversion of an analog input signal results in a corresponding 10-Bit digital number.

The A/D module has high and low-voltage reference input that is software selectable to some combination of VDD, VSS, RA2 or RA3.

The A/D converter has a unique feature of being able to operate while the device is in Sleep mode. To operate in Sleep, the A/D clock must be derived from the A/D’s internal RC oscillator.

 Block Diagram 

Here is the block diagram for the A/D converter in out PIC16F877A microcontroller.

 ADC Special Function Registers 

The A/D module has four registers. These registers are

• A/D Result High Register (ADRESH)
• A/D Result Low Register (ADRESL)
• A/D Control Register 0 (ADCON0)
• A/D Control Register 1 (ADCON1)

The A/D conversion 10-Bit result is stored in (ADRESH+ADRESL) registers.

The operation of the ADC module is completely controlled by (ADCON0+ADCON1) registers.

ADCON0 Register

ADCON1

 Analog Reference 

The A/D module has high and low-voltage reference input that is software selectable to some combination of VDD, VSS, RA2 or RA3. You can select the voltage references in the same way as analog channel selection using the table above.

Let’s assume a V_ref+ of V_DD = 5v and V_ref– of V_ss = 0v for this tutorial. Which results in a full-scale range (FSR) of 5v. Therefore, the A/D conversion resolution will be

 Channel Selection 

In our microcontroller’s ADC module, there are 8 Analog Channels. These channels are multiplexed to a single 1 A/D converter, that’s why an analog switch exists in the block diagram. And you, the programmer, has to select the desired channel before an A/D conversion is initiated.

The ADCON1 and TRIS registers control the operation of the A/D port pins. The port pins that are desired as analog inputs must have their corresponding TRIS bits set (input). If the TRIS bit is cleared (output), the digital output level (V_OH or V_OL) will be converted. The A/D operation is independent of the state of the (CHS2:CHS0) bits and the TRIS bits.

 A/D Aquisition Time 

After the A/D module has been configured as desired, the analog signal of the selected channel must be acquired before the conversion is started. The analog input channels must have their corresponding TRIS bits selected as inputs. After this acquisition time has elapsed, the A/D conversion can start.

For the A/D converter to meet its specified accuracy, the charge holding capacitor (C_HOLD) must be allowed to fully charge to the input channel voltage level.

The maximum recommended impedance for analog sources is 2.5 kΩ. As the impedance is decreased, the acquisition time may be decreased. After the analog input channel is selected (changed), this acquisition must be done before the conversion can be started.

To calculate the minimum acquisition time T_ACQ, you can use the equation below. This equation assumes that 1/2 LSB error is used (1024 steps for the A/D). The 1/2 LSB error is the maximum error allowed for the A/D to meet its specified resolution.

This equation is derived depending on the analog input model circuitry in the diagram below. And you can optimize your system for much lower acquisition time by a little bit more investigation in this model. Alternatively, you can shoot for a safe value instead.

 A/D Conversion Clock Selection 

The A/D conversion time per bit is defined as T_AD. The A/D conversion requires a minimum of 12 T_AD per 10-bit conversion. The source of the A/D conversion clock is software selected. The seven possible options for T_AD are:

• 2 T_OSC
• 4 T_OSC
• 8 T_OSC
• 16 T_OSC
• 32 T_OSC
• 64 T_OSC
• Internal A/D module RC oscillator (2-6 µs)

For correct A/D conversions, the A/D conversion clock (TAD) must be selected to ensure a minimum T_AD time of 1.6 µs. The table below shows the resultant TAD times derived from the device operating frequencies and the A/D clock source selected.

 Starting A/D Conversion 

Setting the GO/DONE bit starts a new conversion for the selected channel. A new conversion should not start before the Aquisition Time T_ACQ has elapsed.

Clearing the GO/DONE bit during a conversion will abort the current conversion. The A/D Result register pair will NOT be updated with the partially completed A/D conversion sample. That is, the (ADRESH:ADRESL) registers will continue to contain the value of the last completed conversion (or the last value written to the ADRESH:ADRESL registers). After the A/D conversion is aborted, the next acquisition on the selected channel is automatically started. The GO/DONE bit can then be set to start the conversion.

The figure below indicates the A/D conversion cycles that it takes to convert an analog signal since setting the GO/DONE bit until the result is written to the ADRES registers. Also note that after the GO bit is set, the first time segment has a minimum of T_CY and a maximum of T_AD.

 A/D Conversion Sequence Timing 

The following diagram will show you the A/D conversion sequence and will also indicate the timing terminology. The acquisition time T_ACQ is the time that the A/D module’s holding capacitor is connected to the external voltage level.

Then there is the conversion time T_C of 10 T_AD, which is started when the GO bit is set. The sum of these two times is the sampling time T_S. Hence, the sampling frequency F_S = 1 / T_S.

There is a minimum acquisition time to ensure that the holding capacitor is charged to a level that will give the desired accuracy for the A/D conversion.

 A/D Conversion Result Registers 

The (ADRESH:ADRESL) register pair is the location where the 10-bit A/D result is loaded at the completion of the A/D conversion. This register pair is 16 bits wide. The A/D module gives the flexibility to left or right justify the 10-bit result in the 16-bit result register.

The A/D Format Select bit (ADFM) controls this justification. The figure below shows the operation of the A/D result justification. Where the extra bits are loaded with ‘0’s.

 Maximum Sampling Rate 

Maximizing the sampling rate of your ADC is obviously a hard task to go for. However, in some situations, you’ll actually need to get as many samples as you can out of your ADC. So, here are a few things to consider.

Analog channel switching requires additional wait time “Aquisition Time T_ACQ“. So, if all that you need is a single channel, then you can save so much time as there is no need to switch between channels and unnecessarily waste so much time waiting for C_HOLD to charge each time.

Another thing, you can sacrifice the accuracy of your ADC conversion reading for pushing the maximum sampling rate a little bit further. 

The A/D converter allows you to make the trade-off of conversion speed to resolution. Regardless of the resolution required, the acquisition time is the same. To speed up the conversion, the clock source of the A/D module may be switched so that the T_AD time violates the minimum specified time (Shown previously, T_ADmin = 1.6µs).

Once the T_AD time violates the minimum specified time, all the following A/D result bits are not valid. The clock sources may only be switched between the F_OSC derived options (cannot be switched from/to RC). The equation to determine the time before the oscillator can be switched is as follows:

Conversion time T_C = T_AD + N • T_AD + (11 – N)(2T_OSC)
Where N = number of bits of resolution required

Since the T_AD is based on the device oscillator, you must use a method (a timer, software loop, etc.) to determine when the A/D oscillator may be changed.

The following example in the table below shows a comparison of time required for a conversion with 4-bits of resolution, versus the 10-bit resolution conversion. The example is for devices operating at 20MHz (The A/D clock is programmed for 32T_OSC) and assumes that immediately after 6T_AD, the A/D clock is programmed for 2T_OSC. The 2T_OSC violates the minimum T_AD time since the last 4 bits will not be converted to correct values. And that’s the trick for speeding it up!

 

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   Configuring ADC With PIC MCU   

 

 Steps To Configure The ADC Module 

To do an A/D Conversion, Follow these steps:

1. Configure the A/D module

• Configure analog pins/voltage reference and digital I/O (ADCON1)
• Select A/D input channel (ADCON0)
• Select A/D conversion clock (ADCON0)
• Turn on A/D module (ADCON0)

2. Configure A/D interrupt (if desired):

• Clear ADIF bit
• Set ADIE bit
• Set PEIE bit
• Set GIE bit

3. Wait the required acquisition time.

4. Start conversion

• Set GO/DONE bit (ADCON0)

5. Wait for A/D conversion to complete by either:

• Polling for the GO/DONE bit to be cleared (interrupts disabled); OR
• Waiting for the A/D interrupt

6. Read A/D Result register pair (ADRESH:ADRESL), clear bit ADIF if required.

7. For the next conversion, go to step 1 or step 2 as required. The A/D conversion time per bit is defined as T_AD.

 Implementing Simple ADC Driver 

 Step1  Configure The ADC Module

All Analog Channels Are Activated, Vref+ = Vdd, Vref- = Vss

Our Fosc = 4MHz, so we’ll choose the ADC clock to be F_OSC/8, so 8T_OSC = 2μs. Which satisfies the condition of T_AD must be larger than 1.6μs.

And finally, Turn ON the ADC module

Let’s set the A/D conversion result justification to be “Right-Justified”

Let’s select AN0 channel for example

 Step2  Configure A/D interrupts (if desired)

 Step3  Wait The Required Aquisition Time T_ACQ

 Step4  Start The A/D Conversion

 Step5  Wait for A/D conversion to complete by either

1. Polling The GO/DONE Bit

2. Respond To The Interrupt Signal!

Alternatively, if you’re using interrupts, you’ll have to do the following

 Step6  Read A/D Result register pair (ADRESH:ADRESL)

 

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   LED Dimmer – ADC LAB1   

 

Lab Name	Analog Input – Analog Output (LED Dimmer) – ADC+PWM
Lab Number	21
Lab Level	Beginner
Lab Objectives	Learn how to configure The ADC Module and read analog signals. Combine the analog readings from a potentiometer with PWM to control LED brightness.

 

       1. Coding       

 

Open the MPLAB IDE and create a new project name it “ADC_LED_Dimmer”. If you have some issues doing so, you can always refer to the previous tutorial using the link below.

Set the configuration bits to match the generic setting which we’ve stated earlier. And if you also find troubles creating this file, you can always refer to the previous tutorial using the link below.

Now, open the main.c file and let’s start developing the firmware for our project.

The first task is to initialize the ADC and PWM modules using the basic firmware drivers which we’ve already built previously. Then, we’ll read convert the voltage level on Analog Channel 0 and send the 10-Bit A/D conversion result as a Duty Cycle for PWM1. So the brightness of the LED is determined by the analog input for Channel 0.

Here is the Full Code Listing For This LAB

 

       2. Simulation       

 

Here is an animation for the running simulation tests.

 

       3. Prototyping       

 

Wiring up this schematic on a breadboard should be an easy task. Just upload your firmware hex file to the microcontroller chip. And hook up the input power rails and start testing it up!

Here is a video for the final output of this LAB.

If you’ve any troubles or got stuck at any point, just drop me a comment. I’ll be always here and ready for help. Or even other readers may do a better job in this.

 

Download LAB Project

 

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   Finger Snap Switch – ADC LAB2   

 

Lab Name	Finger Snap Switch
Lab Number	22
Lab Level	Intermediate
Lab Objectives	Learn how to configure The ADC module and read analog signals. Identify sound intensity (loudness) in order to flip a LED when a finger snap is captured by a microphone!

 

       1. Coding       

 

Open the MPLAB IDE and create a new project name it “ADC_Microphone”. If you have some issues doing so, you can always refer to the previous tutorial using the link below.

Set the configuration bits to match the generic setting which we’ve stated earlier. And if you also find troubles creating this file, you can always refer to the previous tutorial using the link below.

Now, open the main.c file and let’s start developing the firmware for our project.

The first task is to initialize the ADC module using the basic firmware driver which we’ve already built previously. Then, we’ll continuously convert & read the voltage level on Analog Channel 0 (The Microphone Amplified Output) and compare 10-Bit A/D conversion against a specific threshold value. So we can detect any loud sound nearby and flip an LED as a result.

Here is The Full Code Listing For This Project

Note!

Note: You should know that the output audio signal captured by the microphone will be a few milli-volts in magnitude! That’s almost identical to the resolution of our ADC, therefore it’s impossible to capture such a signal. Hence, we’ll have to build a very basic amplifier to give this signal a constant gain. Here is the simplest common-emitter amplifier that you can build with a transistor and a few resistors.

 

       2. Prototyping       

 

And here is a video for the final output of this LAB.

If you’ve any troubles or got stuck at any point, just drop me a comment. I’ll be always here and ready for help. Or even other readers may do a better job in this.

 

Download LAB Project

 

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   Different Schemes To Read ADC   

 

 Single Channel Conversion 

1 One Shot

The one-shot scheme of conversion is basically what we’ve done so far in a previous couple of LABs. The A/D converter is activated and ready for conversion, and if you need to convert a specific analog channel, you’ll call the ADC_Read routine. Consequently, the A/D will switch over to the desired analog channel and a conversion process will be initiated until the result is ready.

This scheme can be used for many applications, specifically low power applications. Which requires low sampling rate A/D conversion. You can set up a timer interrupt and initiate A/D conversions as periodic one-shot conversions.

Sometimes, this scheme will not be sufficient by any means. And I confirm that your ADC is capable of more! it can produce a much higher sampling rate if your application needs to.

2 Continuous Mode

This mode is an automatic self-triggering continuous series of A/D conversions. In this way, you’ll push your ADC to its limits and go far near the maximum sampling rate possible.

You can set up A/D interrupt and self-trigger the ADC after reading each sample. As you know, switching channels require waiting some time which is something that you don’t want. Provided that your target is to shoot for the maximum possible A/D sampling rate.

To give you an idea of how this can be implemented, here is a code snippet for the ISR in this case

Please, be advised that this scheme maximizes your overall ADC’s sampling rate. However, you should know that you’re sacrificing CPU time which is going to be overloaded by the excessive amount of interrupts. This “interrupts jitter” is obviously proportional to the current sampling rate of your ADC + any other interrupt sources!

 Multiple Channels Conversion 

1 Burst of Conversions

In some situations, your microcontroller will have to read multiple analog channels. And as we know that there is only 1 A/D resource. That’s why we have to configure the analog channel selection switch before issuing an A/D conversion.

One way to get this task done is to do a burst of conversions in a row for all your analog channels. In this way, you’ll be able to sequentially convert all your channels in a row. Here is a typical implementation for a burst conversion routine.

2 Continuous Bursts

Obviously, you can set up the A/D converter interrupt signal in order to continuously update your analog channels result buffer sequentially. And the “interrupt jitter” problem will also arise in this case.

 

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   Concluding Remarks   

 

  1  

How To Measure Voltage Greater Than Vcc (>5v)

You can just attenuate the original signal by using a proper attenuator or maybe a voltage divider! a couple of resistors will give your ADC much higher upper limit for conversion.

Using R & R resistors, you’ll make your ADC capable of reading up to 10volts. Similarly, using R & 3R, you’ll be able to read signals up to 20volts. Just Apply Voltage Divider Rule.

What you should notice is the fact that the accuracy is dropping significantly as we go up. The lower the voltage is, the less error generated by the A/D measurement setup.

  2  

How To Measure Small Signals (~mv)

Designing a suitable amplifier for your system will make the job of A/D converter much easier. Sometimes a simple common emitter amplifier will do the trick. Even an op-amp can do much help.

However, sometimes you may need something different. Here is an example, instead of trying to measure too very small signals to check the difference between them. You just can use a differential amplifier and amplify this difference between the signals. Now the job of our ADC is much easier than before! And so on…

  3  

Converting ADC Result Back To Voltage

After a successful A/D conversion, you can work it in reverse to calculate back the original voltage level. This only requires the knowledge of your ADC’s current resolution Q.

For 10-Bit ADC with FSR=5v, assume a digital result of conversion ANRES = 256

Then the analog corresponding voltage is calculated as shown below

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Regards,

Khaled M.

 

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