Editor’s note: This is the last post in a three-part ENOB blog series. You can find the two previous parts here: And then there was noise: The mystery of the missing ENOB, Part 2 and And then there was noise: The mystery of the missing ENOB if you missed it.
Sheets of heavy rain pound the pavement outside.
Arcs of lightning crackle in the distance.
A shadow fills the doorframe.
The eyes glow red.
It moves forward, boots thumping menacingly.
“It’s the eyes!” PGA shrieks. “The eyes I saw just before ENOB disappeared!”
The shadow takes another step toward the light.
“He did something to ENOB – or at least he knows what happened to him!” PGA yells.
Another step forward.
Another menacing THUMP.
PGA swallows hard, then sputters: “W-Who are you?”
The shadow steps into the light.
He’s got a deeply lined face.
Eyes like embers.
A gravelly voice splinters the stunned silence.
Defiantly, PGA steps in front of the stranger. “What did you do to ENOB?”
Input-Referred Noise brushes past PGA.
He waves to the bartender for a drink.
He takes a seat at a table.
Staring off into the darkness of the room and his memories, the man begins.
“ENOB … always spouting off nonsense about being the best resolution metric. I’ve been chasing that punk for years, trying to set the record straight.”
Input-Referred Noise takes a long, slow sip of his drink.
“I heard whispers he was lying and cheating his way across town. I finally tracked him here. I waited for just the right moment and –”
“You killed him, didn’t you?” PGA shouts. He glares at the others. “I told you guys I had nothing to do with this!”
Input-Referred Noise rolls his eyes: “Don’t be so dramatic, PGA. I didn’t do anything to ENOB – he bolted like a coward before I got the chance. He got nervous when you guys called him out on the resolution of the 10mV bridge signal. He knew it’d make him look bad, and he panicked.”
He sips again.
“Fortunately for him, the lights go out and he disappears in the confusion. I followed him out the back, but he was already gone.”
Multiplexer stands up: “Great – ENOB’s gone. One mystery solved. But that doesn’t explain what happened to the bits – did he take them?”
“That’s a good question.” Input-Referred Noise motions to the bartender. “Give me a napkin and a pen.”
As the crowd gathers around, he draws out an equation on the napkin.
“As you can see, ENOB is dependent on the full-scale range (FSR) and root-mean-square (RMS) input-referred noise. So, if VREF is 2.5V, gain is 1 and the measured noise is 150nVRMS at 2.5SPS, you get 25 ENOBs.”
“But it’s important to note that because of this ratio, ENOB is easily manipulated by modifying the reference voltage. In fact, the same input-referred noise with a 5V reference increases ENOB to 26!”
“However, when your input doesn’t use the FSR, like with the bridge signal you originally sampled, ENOB takes a huge hit,” the stranger continues.”
“With your 10mV full-scale signal, 5V reference and gain of 1, your actual resolution is 16 bits, not 26 as ENOB claimed. But again, the RMS noise remains the same.”
Input-Referred Noise stands up.
“You want to know where the bits went? My guess is he never even had 26 bits in the first place.”
Shocked whispers ripple through the crowd.
Op Amp steps forward. “That’s all well and good, but even after ENOB disappeared, we lost more bits when we tried to gain up the signal with an external amplifier. How do you explain that?”
Input-Referred Noise calmly looks around, then locks his gaze on PGA.
“PGA – what’s your voltage-noise spectral density?”
“7nV√Hz across frequency.”
“What’s yours, Op Amp?”
Input-Referred Noise raises an eyebrow. “What’s your noise spectral density in the 1/f region?”
Op Amp’s eyes grow wide. Then, quietly he murmurs:
The crowd gasps.
Temp Sensor faints.
Input-Referred Noise shakes his head.
“And there’s your problem. When you’re measuring slow-moving signals like a load-cell output, your frequencies of interest are in the 1/f region of the amplifier’s voltage-noise spectral-density curve. But a lot of amplifiers specify voltage-noise spectral density around 1kHz, which isn’t relevant here.”
Input-Referred Noise puts his hand on Op Amp’s shoulder, then turns to the crowd.
“For example, in Op Amp’s case, if you assume an effective noise bandwidth of 1Hz, you’re gaining up to 50nVRMS of noise at the input of the analog-to-digital converter (ADC). If you used a programmable gain amplifier (PGA) with no external amp, you’d only be gaining up 7nVRMS of noise.
That gives you better resolution , even with less gain .”
Op Amp cries out: “I’m sorry, brother! Maybe if I was chopper-stabilized, things would be different.”
“It’s okay, big guy,” reassures Input-Referred Noise. “We all have our place in life. Yours just isn’t in front of a high-precision, low-noise, delta-sigma ADC.”
The stranger finishes his drink, pays the bartender, then turns to leave.
“Where are you going?” PGA asks.
Input-Referred Noise gazes out the windows with tired eyes.
Outside, the clouds break.
The sun slices through the blinds.
The light cuts across his face like battle scars.
He takes a deep breath.
“ENOB’s out there somewhere. I bet he’s halfway to the next town by now, looking for more well-meaning people to believe his lies. And the only thing that’s going to stop him is me – a straight-shooting absolute value who always tells it like it is. He can run, he can hide, but wherever ENOB goes –”
And with that, our story has come to an end. However, the battle for legitimacy rages on, as the myths surrounding ENOB persist. Will you join the fight and spread the word that input-referred noise is the best metric for specifying ADC resolution? If yes, please check out these other resources in your quest for truth; justice; and high-precision, low-noise ADCs.
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- Read more delta-sigma ADC blog posts.
- Download the e-book, Best of Baker’s Best: Delta-Sigma ADCs.*
- Find commonly used analog design formulas in the Analog Engineer’s Pocket Reference* e-book.
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