ADC - Analog to Digital Converter ( Basic ) [ADC_BASIC]

This element is used to model the effects of analog to digital conversion on the RF path. This output from this model is analog rather than a digital binary output. This model can really be thought of as a non-ideal ADC followed by an ideal DAC so we have analog output. The output spectrum is a continuous frequency spectrum representing the 1st Nyquist zone (0 to Sample Rate / 2 Hz). All input spectrum will be aliased into the 1st Nyquist zone. The Signal to Noise Ratio (SNR) is used to determine the effective noise figure contribution of the ADC. A good reference on ADC basics can be found in application note, "Basics of Designing a Digital Radio Receiver (Radio 101)", Brad Brannon, Analog Devices, Inc.

NOTE: The port on the ADC output should have the same impedance as the ADC to eliminate impedance mismatch effects on the data.

 

Models and Symbols

 

Name

Model

ADC_BASIC

Alternate Models

 

Schematic Symbol

ADC_S

Alternate Schematic Symbols

None

 

Model Parameters

Parameter

Description

Units

Default Value

Bits

Number of Bits

 

12

FS

Sampling Frequency

MHz

40

Vrange

Analog Input Voltage Range

Vpp

2

SNR

Signal to Noise Ratio

dBFS

70

Rin

Input Resistance

Ohm

200

Cin

Input Capacitance

pF

5

 

Additional Parameter Information:

 

Number of Bits

This is the number of bits used by the ADC. The theoretical SNR = Number of Bits x 6 dB.

 

Sampling Frequency

This the frequency at which the ADC is sampled. The Nyquist frequency = Sampling Frequency / 2. This model assumes that the external clock is ideal and does not affect the SNR. For non-ideal clocks include the performance degradation in the SNR.

 

Analog Input Voltage Range

This the peak to peak input voltage range of the ADC. The full scale voltage is determined from this parameter as Vrms full scale = Vrange / (2 * sqrt(2) ).

 

Signal to Noise Ratio

The signal to noise ratio of the ADC is specified relative to the full scale rms voltage of the ADC. NOTE: When examining the performance of an ADC in SPECTRASYS the carrier to noise ratio of the simulation and ADC will only be equivalent when there are no other alias signals that fall within the channel and the peak signal value is equivalent to the full scale voltage of the ADC.

 

Input Resistance

This is the input resistance of the ADC.

 

Input Capacitance

This is the shunt input capacitance of the ADC.

 

Additional Operation Information:

 

Noise Figure

The noise figure of the ADC is determined according to the following formula.

NF (dB) = Full Scale Pin (dBm) - SNR (dB) - 10 Log ( FS / 2 ) - Thermal Noise Power (dBm/Hz)

where Full Scale Pin (dBm)  = 10 Log ( Vin^2 / Zin ) + 30 and Thermal Noise Power (dBm/Hz) = 10 Log ( kT ) + 30, Vin in rms, k is Boltzmann's constant and T is temperature in Kelvin

 

Broadband Input Noise

Broadband input noise from all Nyquist zones will be aliased into the ADC baseband output. Consequently, the final noise figure of the ADC will be affected by the noise filtering of the input signals and noise as in the real world. Note: If no filtering is provided ahead of the ADC then the noise performance of the ADC can be affected by the bandwidth of the noise as defined by the 'Ignore Frequency Above' and 'Ignore Frequency Below' parameters in the System Analysis since these limits determine the range of broadband noise.

 

Gain

This gain of the ADC is very close to 1 or 0 dB when the output is terminated in the same resistance as the input resistance. When the input resistance is changed the ADC load impedance must also be changed to keep the gain at 0 dB.

 

Output Impedance

It is assumed that the ADC is does not change impedance from input to output. Consequently, the load impedance should always be the same as the input resistance.

 

Spectrum Identification

SPECTRASYS will show ADC identification information for spectrums at the output of the ADC. An example is given below. In the equation in [] brackets the 'Nyq:x' identifies the originating Nyquist zone. In this example the 'Source' signal came from the 3rd Nyquist zone. A + or - sign will appear before the Nyquist zone indicator to identify inverted aliased spectrum. In this case the spectrum originated in an odd Nyquist zone so there is no spectrum inversion. The elements after the equation indicate the path the signal took to get to the ADC output.

 

 

Some ADC Basics

Nyquist requires that signal be sampled at twice the bandwidth of the signal. Therefore, if the signal bandwidth is 1 MHz, then sampling at 2 MHz is sufficient. Anything beyond this is called Over Sampling. Under sampling is the act of sampling at a frequency much less than half of the actual signal frequency. Consequently, it is possible to both over sample and under sample at the same time since one is defined with respect to the bandwidth and the other at the desired frequency.

 

The faster a signal is sampled, the lower the noise floor because the noise is spread over more frequencies. The noise floor (referenced to the full scale value of the ADC) is:

 

Noise Floor (dBFS) = 6.02 * Bits + 1.76 + 10 Log ( Fsample rate / 2 )

 

Note that each time the sample rate is doubled the noise floor improves by 3 dB. Since digital filtering removes unwanted noise and spurious signals the SNR of the ADC may be greatly improved by filtering just the bandwidth of the desired signal. Therefore, the SNR is proportional to 10 Log ( Fsample rate / Filter BW ). The greater the ratio between sample rate and filter bandwidth the higher the SNR.

 

Analog input ranges are divided up into Nyquist zones. The most common is the first Nyquist zone which goes from DC to one half the sampling frequency (FS). The 2nd Nyquist zone is from FS / 2 to FS, 3rd is from FS to 3 FS / 2, etc., etc. A unique and useful effect of using higher Nyquist zones is that signals sampled in higher zones are mirrored down to the first Nyquist zone once digitized. When input signals appearing in even Nyquist zones are down converted they are spectrally inverted.

 

DC Block - DC is not blocked.

WARNING: Only the linear portion of this model is used by simulators other than Spectrasys.