lesson
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How do modern oscilloscopes capture high-speed waveforms at billions of samples per second? They compare an incoming analog voltage to every possible threshold level simultaneously in a single clock cycle.
To perform this instant conversion, an n-bit Flash Analogue-to-Digital Converter (ADC) relies on a potential divider chain of 2n identical resistors of equal resistance R, known as a reference voltage ladder.
The Ladder Architecture
To resolve an analog input into 2n digital states, the architecture requires 2n−1 op-amp comparators connected in parallel to test the signal against every tap voltage simultaneously.
To provide these thresholds, the circuit uses a potential divider chain of 2n identical resistors of equal resistance R connected across Vref to ground.
📊Interactive diagram
How do we derive the exact voltage at each comparator tap node?
Deriving the Node Voltages
In 1827, Georg Ohm demonstrated that current through a conductor is proportional to the potential difference across it. Because identical resistors in series share the same current, each resistor drops an identical slice of voltage.
The total resistance of a ladder with N=2n matched resistors is Rtotal=2n⋅R.
Applying Ohm's law gives the steady ladder current: I=RtotalVref=2nRVref
The voltage at tap k (measured across k resistors from 0 V ground) is the product of current I and cumulative resistance k⋅R: Vk=I⋅(k⋅R)=(2nRVref)⋅(k⋅R)=(2nk)Vref
📊Interactive diagram