Agilent Spectrum Analysis Basics - Agilent Technologies

2D dB 3D dB
3D dB 3D dB
With a constant LO level, the mixer output is linearly related to the input
signal level. For all practical purposes, this is true as long as the input signal
is more than 15 to 20 dB below the level of the LO. There are also terms
involving harmonics of the input signal:
(3k 3 /4)V LO V 1 2 sin(ω LO – 2 ω 1 )t,
(k 4 /8)V LO V 1 3 sin(ω LO – 3ω 1 )t, etc.
These terms tell us that dynamic range due to internal distortion is a
function of the input signal level at the input mixer. Let’s see how this works,
using as our definition of dynamic range, the difference in dB between the
fundamental tone and the internally generated distortion.
The argument of the sine in the first term includes 2ω 1 , so it represents
the second harmonic of the input signal. The level of this second harmonic
is a function of the square of the voltage of the fundamental, V 1 2 . This fact
tells us that for every dB that we drop the level of the fundamental at the
input mixer, the internally generated second harmonic drops by 2 dB.
See Figure 6-1. The second term includes 3ω 1 , the third harmonic, and the
cube of the input-signal voltage, V 1 3 . So a 1 dB change in the fundamental
at the input mixer changes the internally generated third harmonic by 3 dB.
Distortion is often described by its order. The order can be determined by
noting the coefficient associated with the signal frequency or the exponent
associated with the signal amplitude. Thus second-harmonic distortion is
second order and third harmonic distortion is third order. The order also
indicates the change in internally generated distortion relative to the change
in the fundamental tone that created it.
Now let us add a second input signal:
v = V LO sin(ω LO t) + V 1 sin(ω 1 t) + V 2 sin(ω 2 t)
This time when we go through the math to find internally generated distortion,
in addition to harmonic distortion, we get:
(k 4 /8)V LO V 1 2 V 2 cos[ω LO – (2 ω 1 – ω 2 )]t,
(k 4 /8)V LO V 1 V 2
2 cos[ω LO – (2 ω 2 – ω 1 )]t, etc.
D dB
D dB
D dB
w 2 w 3 w 2w 1
– w 2
w 1
w 2
2w 2
– w 1
Figure 6-1. Changing the level of fundamental tones at the mixer
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