Image Frequency & I/Q Image Rejection
For a superheterodyne downconverter, the signal at the image frequency mixes to the same IF as the wanted signal. This tool gives the LO and image frequencies for high- or low-side injection, and the image-rejection ratio (IRR) achievable in an I/Q (Hartley/Weaver) receiver limited by gain and phase imbalance between the I and Q paths.
Equations & Parameters ▸
\(f_{\text{LO}} = f_{\text{RF}} \pm f_{\text{IF}} \qquad f_{\text{image}} = f_{\text{RF}} \pm 2 f_{\text{IF}}\)
\(\text{IRR} = 10\log_{10}\dfrac{1 + A^2 + 2A\cos\theta}{1 + A^2 - 2A\cos\theta},\quad A = 10^{\,\Delta g/20}\)
\(\text{IRR} = 10\log_{10}\dfrac{1 + A^2 + 2A\cos\theta}{1 + A^2 - 2A\cos\theta},\quad A = 10^{\,\Delta g/20}\)
| fRF | Wanted RF (signal) frequency (MHz). |
| fIF | Intermediate frequency (MHz). |
| LO side | High-side (LO above RF) or low-side (LO below RF) injection. |
| Δg | I/Q amplitude (gain) imbalance (dB). |
| θ | I/Q phase imbalance — deviation from 90° (degrees). |
| IRR | Image-rejection ratio: how far the image is suppressed below the wanted signal. |
References: B. Razavi, RF Microelectronics, 2nd ed., Prentice Hall, 2012. · R. C. Sanderson & J. Hong; ADI MT-088, Analog Devices Mixer Tutorial.
Inputs
MHz
Wanted signalMHz
Intermediate freqInjection
dB
I/Q gain errordeg
I/Q phase errorResults
Frequencies
LO frequency—
Image frequency—
Image rejection
IRR—
Diagram