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LTC1409

APPLICATIONS INFORMATION

Signal-to-Noise Ratio

The signal-to-noise plus distortion ratio [S/(N + D)] is the

ratio between the RMS amplitude of the fundamental input

frequency to the RMS amplitude of all other frequency

components at the A/D output. The output is band limited

to frequencies from above DC and below half the sampling

frequency. Figure 2 shows a typical spectral content with

an 800kHz sampling rate and a 100kHz input. The dynamic

performance is excellent for input frequencies up to and

beyond the Nyquist limit of 400kHz.

Effective Number of Bits

The Effective Number of Bits (ENOBs) is a measurement of

the resolution of an ADC and is directly related to the

S/(N + D) by the equation:

N = [S/(N + D) – 1.76]/6.02

where N is the effective number of bits of resolution and

S/(N + D) is expressed in dB. At the maximum sampling

rate of 800kHz the LTC1409 maintains near ideal ENOBs

up to the Nyquist input frequency of 400kHz. Refer to

Figure 3.

THD

+++…

20 Log

222

where V1 is the RMS amplitude of the fundamental fre-

quency and V2 through Vn are the amplitudes of the

second through Nth harmonics. THD vs input frequency is

shown in Figure 4. The LTC1409 has good distortion

performance up to the Nyquist frequency and beyond.

INPUT FREQUENCY (Hz)

100k

10M

LTC1409 • F03

10k

fSAMPLE = 800kHz

Figure 3. Effective Bits and Signal/(Noise +

Distortion) vs Input Frequency

Total Harmonic Distortion

Total Harmonic Distortion (THD) is the ratio of the RMS sum

of all harmonics of the input signal to the fundamental itself.

The out-of-band harmonics alias into the frequency band

between DC and half the sampling frequency. THD is

expressed as:

Figure 4. Distortion vs Input Frequency

Intermodulation Distortion

If the ADC input signal consists of more than one spectral

component, the ADC transfer function nonlinearity can

produce intermodulation distortion (IMD) in addition to

THD. IMD is the change in one sinusoidal input caused by

the presence of another sinusoidal input at a different

frequency.

If two pure sine waves of frequencies fa and fb are applied

to the ADC input, nonlinearities in the DC transfer function

can create distortion products at the sum and difference

frequencies of mfa + –nfb, where m and n = 0, 1, 2, 3, etc.

For example, the 2nd order IMD terms include (fa + fb). If

the two input sine waves are equal in magnitude, the value

(in decibels) of the 2nd order IMD products can be

expressed by the following formula:

IMD fa

() = 20 Log

Amplitude at (fa + fb)

Amplitude at fa

Peak Harmonic or Spurious Noise

The peak harmonic or spurious noise is the largest spec-

tral component excluding the input signal and DC. This

INPUT FREQUENCY (Hz)

–10

–20

–30

–40

–50

–60

–70

–80

–90

–100

100k

10M

LTC1409 • F04

10k

THD

3RD

2ND

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