LMX8410L: mixing spurs

Hello Takahashi-san,

Noriyuki Takahashi said:

Q1. Can the definition of 2x2 spur, 3x3 spur as described on 3.6 be as follows?

2x2 spur = the mixed signal of the second RF harmonic and the second LO harmonic

3x3 spur = the mixed signal of the third RF harmonic and the third  LO harmonic

Correct

Noriyuki Takahashi said:

Q2. If Q1's understanding is correct, are equations as below correct? In this case, they assume RF input frequency = F1, LO input frequency = F2 and F1 = F2 for simplicity.

1x1 spur : F1 + F1＝2×F1   --- (1) Undesired Signal

                F1 - F1＝0＝DC1　--- (2)  Desired Signal

2x2 spur : 2×F1 + 2×F1＝4×F1   ---(3) Undesired Signal

                2×F1 - 2×F1＝0＝DC2　---(4) Undesired Signal

3x3 spur : 3×F1 + 3×F1＝6×F1   --- (5) Undesired Signal

                  3×F1 - 3×F1＝0＝DC3　--- (6) Undesired Signal

As long as F1 == F2, these equations seem correct to me. However, this use case is uncommon.

Noriyuki Takahashi said:

Q3. If Q2's understanding is correct,  does 2x2 spur that is described on 3.6  mean equation (2)? And 3x3 spur that is described on 3.6  mean equation (5)?

2x2 spur of 3.6 refers to (4), since this is twice the IF frequency (in this case, 2 * (F1 - F1)). 3x3 spur would correspond to (6), since it is three times the IF frequency (3 * (F1 - F1)). Equations (1), (3), (5) refer to a frequency that is well beyond the bandwidth of the IF amplifier and which will not be detectable in this case.

Noriyuki Takahashi said:

And if this understanding is correct,   can the sentence on 3.6 as below and figure 8&9 be proven by equation (2)&(3)? 

"In fact, the mixing spurs from the LMX8410L are almost negligible."

When we measured the 2x2 spur and the 3x3 spur, it was not the case that F1 == F2. This is critical to understanding why the sentence in 3.6 is so impactful. The spurs are not at DC, but at some measurable frequency, often within the expected downconversion bandwidth of the IF output. For example, if F1 = 8.1GHz and LO = 8GHz, the graph suggests that measurement of the IF output at 200MHz yields about -70dBc, and at 300MHz yields about -80dBc. A 14-bit ADC extracting an IF signal from even a relatively high-power carrier could maybe barely detect the 2x2 spur, and will likely completely miss the 3x3 spur. In practice, the carrier power is often very low (-10dBm) and the spurs are well below the measurement floor.

Noriyuki Takahashi said:

Q4. How should they understand equation (4) & (5)? (4) & (5) are DC and they are not sure whether they should understand these as mixing spurs. 

For their system, equation (2) is important, though.

To summarize again: (1), (3), and (5) are very high frequency and will be filtered by the bandwidth of the IF amplifier. (2) is the conventional mixer downconversion product. (4) is the 2x2 spur. (6) is the 3x3 spur. Both (4) and (6) are very low power as shown in the figures in 3.6, and can almost always be considered negligible.

Regards,

Derek Payne