IEEE Solid-States Circuits Magazine - Spring 2020 - 48

The main idea behind time encoding consists of
representing an analog signal with a modulated
square wave, where the signal information
is encoded in the transitions instead of in
the instantaneous amplitude.
worldwide have been published in
application domains such as sensor
readout [7]-[10], telecom [11]-[13],
wideband wireless [14]-[18], the Internet of Things [19], automotive [20],
[21], and biomedical [22] -[24], to
name a few. Note that the integrat--
ing properties of VCOs have also
been used to implement continuoustime filters, time-to-digital converters,
and other analog signal processing
blocks [25]-[27].
The main idea behind time encoding consists of representing an analog signal with a modulated square
wave, where the signal information is
encoded in the transitions instead of
in the instantaneous amplitude. Such
a signal is easy to handle with digital

circuits and robust against noise and
distortion. Representing the analog signal information is, then, done through
pulse modulations. Pulsewidth modulation (PWM) is one of the best examples and is used extensively in, for
instance, power electronics. The typical block diagram of a time-encoding
ADC is shown in Figure 1. The analog
input signal is applied to a pulse modulator that encodes the information
in the pulsewidth, frequency, or position of a signal (or set of signals) with
two levels only. This two-level signal, which is still analog, is sampled
afterward at a sampling frequency fs ,
typically much larger than the input
signal bandwidth ABW. Differing from
conventional ADCs, the sampler can

VCO-Based Analog-to-Digital
Conversion: Basic Principles

fs
Pulse
Modulator

Decoder
(Low-Pass
Filter)

D Q

FIGURE 1: The principle signal operations in a time-encoding ADC.

Sampling Clock
Reset

VCO

Clock

Counter

.
.
.

ADC
Output

FIGURE 2: The conceptual block diagram of an open-loop VCO-based ADC with a counter.

S P R I N G 2 0 2 0

IEEE SOLID-STATE CIRCUITS MAGAZINE

now be a simple flip-flop, as the signal
has only two values. From the sampled
square wave, a decoder can reconstruct a multibit approximation of the
analog input signal, which is typically
done with a digital low-pass filter.
Although early time-encoding ADCs
used PWM [1], [2], PWM may not be the
best option to replace analog circuits
in an ADC. Indeed, PWM modulators
require sawtooth generators or analog
filters, which are still made of operational amplifiers (op-amps) and other
highly linear circuits [28], [29]. VCObased ADCs, on the other hand, can
be implemented very efficiently with
a ring oscillator, which is a simple
digital circuit [30], [31]. To be precise,
VCO-based ADCs need to be modeled
using a different type of pulse modulation, called pulse-frequency modulation (PFM). PFM exhibits first-order
noise shaping when sampled directly,
contrary to other pulse modulations,
such as PWM. The hardware simplicity and digital nature of ring oscillators and the noise-shaping properties
of PFM have led to VCO-based ADCs'
wide popularity. We will, therefore,
concentrate most of our discussion on
VCO-based ADCs.

So how do VCO-based ADCs digitize
an analog signal? We give an intuitive
explanation of this function without detailed mathematics. Figure 2
depicts the simplest VCO-based ADC
architecture, which is also one of the
most used. A slowly varying input
signal modulates the frequency of
an oscillator (the VCO). The pulses of
the oscillator are then counted with a
digital counter. Assuming a sampling
period Ts = 1/fs, the number of pulses
accumulated in the counter is dumped
into a register every Ts seconds, and
the counter is reset. The value in the
register is therefore a measure of the
VCO frequency and hence of the analog input signal during that sample.
Clearly, the higher the oscillation
frequency compared to the sampling
frequency, the higher the resolution
that can be achieved. This defines

IEEE Solid-States Circuits Magazine - Spring 2020

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