Image response

<h2 id="image-rejection-ratio">Image rejection ratio</h2>
<p>The <i>image rejection ratio</i>, or   <i>image frequency rejection ratio</i>, is the <a href="/facts/Ratio/mFmhQt7T">ratio</a> of the intermediate-<a href="/facts/Frequency/QUSbPaW8">frequency</a> (IF) <a href="/facts/Signal_level/qohClhyG">signal level</a> produced by the desired input frequency to that produced by the <a href="/facts/Image_frequency/S2SA0NCV">image frequency</a>. The image rejection ratio is usually expressed in <a href="/facts/Decibel/0LyxAPXh">dB</a>.  When the image rejection ratio is measured, the input signal levels of the desired and image frequencies must be equal for the measurement to be meaningful. 
</p><p>IMRR is measured in <a href="/facts/Decibel/0LyxAPXh">dB</a>, giving the ratio of the wanted to the unwanted signal to yield the same output from the receiver. In a good design, ratios of >60 dB are achievable. Note that IMRR is not a measurement of the performance of the IF stages or IF filtering (<a href="/facts/Selectivity_(radio)/bS8A1RKL">selectivity</a>); the signal yields a perfectly valid IF frequency. Rather, it is the measure of the bandpass characteristics of the stages preceding the IF amplifier, which will consist of RF bandpass filters and usually an RF amplifier stage or two.
</p>
<h2 id="image-rejection-formulas">Image rejection formulas</h2>
<p>The <i>Image Frequency Rejection Ratio</i> (IRR) is characterized by its RF filter which can be determined on the basis of its relative response of a <a href="/facts/Tuned_Circuit/tzEfI7Hf">parallel tuned circuit</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p><p>
  
    
      
        I
        R
        R
        =
        
          
            1
            +
            
              ρ
              
                2
              
            
            
              Q
              
                2
              
            
          
        
      
    
    {\displaystyle IRR={\sqrt {1+\rho ^{2}Q^{2}}}}

</p><p>where,
</p><p>
  
    
      
        ρ
        =
        
          
            
              f
              
                I
                M
                A
                G
                E
              
            
            
              f
              
                R
                F
              
            
          
        
        −
        
          
            
              f
              
                R
                F
              
            
            
              f
              
                I
                M
                A
                G
                E
              
            
          
        
      
    
    {\displaystyle \rho ={\frac {f_{IMAGE}}{f_{RF}}}-{\frac {f_{RF}}{f_{IMAGE}}}}
  
and Q is the quality factor.
</p><p>The Image Rejection Ratio for a given value of gain imbalance 
  
    
      
        γ
        ,
        (
        ϵ
        =
        γ
        −
        1
        )
      
    
    {\displaystyle \gamma ,(\epsilon =\gamma -1)}
  
 and phase imbalance 
  
    
      
        ϕ
      
    
    {\displaystyle \phi }
  
 is determined by,<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p><p>
  
    
      
        I
        M
        R
        R
        =
        
          
            
              
                γ
                
                  2
                
              
              +
              1
              −
              2
              γ
              c
              o
              s
              (
              ϕ
              )
            
            
              
                γ
                
                  2
                
              
              +
              1
              +
              2
              γ
              c
              o
              s
              (
              ϕ
              )
            
          
        
        ≈
        
          
            
              
                ϵ
                
                  2
                
              
              +
              
                ϕ
                
                  2
                
              
            
            4
          
        
      
    
    {\displaystyle IMRR={\frac {\gamma ^{2}+1-2\gamma cos(\phi )}{\gamma ^{2}+1+2\gamma cos(\phi )}}\approx {\frac {\epsilon ^{2}+\phi ^{2}}{4}}}

</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Image_frequency/S2SA0NCV">Image frequency</a></li></ul>

<p> This article incorporates <a href="/facts/Copyright_status_of_works_by_the_federal_government_of_the_United_States/Q1jvr96g">public domain material</a> from <a href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm"><i>Federal Standard 1037C</i></a>. <a href="/facts/General_Services_Administration/Np3opv9x">General Services Administration</a>. Archived from <a href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 2022-01-22. (in support of <a href="/facts/MIL-STD-188/D5rsvdsW">MIL-STD-188</a>).
</p>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>C-W and A-M Radio Transmitters and Receivers, United States Department of the Army, 1952  page 229
 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Sekhar, T. G. Thomas S. Chandra (2005-08-01). Communication Theory. Tata McGraw-Hill Education. ISBN 9780070590915. <a href="9780070590915" target="_blank">9780070590915</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"Image Rejection Ratio (IMRR) with transmit IQ gain/phase imbalance". www.dsplog.com. 31 January 2013. Retrieved 2018-09-14. <a href="http://www.dsplog.com/2013/01/31/imrr-transmit-iq-gain-phase-imbalance/" target="_blank">http://www.dsplog.com/2013/01/31/imrr-transmit-iq-gain-phase-imbalance/</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Image response open-in-new

Image response