The article compares the sensitivity and spur-free dynamic range of RF receiver designs with the RF filter positioned before or after the RF amplifier. It presents numerical analyses showing that the placement of the filter significantly affects system performance, concluding that moving the RF filter results in degraded sensitivity and spur-free dynamic range. By using specific gain, noise figure, and intercept point values, it calculates and contrasts system metrics in both configurations.

1. Receiver design Trade-Offs
Hamid Kiabi
In this article will compare the sensitivity and spur-free dynamic range when the RF
filter follows the RF amplifier and when the RF filter precedes the RF amplifier.
Figure 1 shows an example of a receiver block diagram. The RF filter protects the mixer
from the image and half IF spurs. Sensitivity and spur free dynamic range are compared
when the filter follows the RF amplifier and when the RF filter precedes the RF
amplifier. The block diagram shows the filter following the RF amplifier.
Numerical values are assigned to each block of the receiver to make the result more
intuitive.
Figure-1 RECEIVER BLOCK DIAGRAM
First, the total gain for the system Gsys is calculated by simply adding all the gains of
each stage together.
Gsys = - 2 + 12 -3 +8 = 21db (1)
Mixer
OSC
BP
Filter
Gain = 12db
NF= 2db
IPi3 = -10dbm
Loss =3db
Gain =8db
NF=4db
IPi3= -10dbm
Loss = 2db
NEB = 15Khz
Gain = 8db
NF=4db
IPi3 = 10dbm
Transmitter
Loss =2db

2. Next the losses in front of the gain stages are combined with those gain stages.
The six stage network combines into a three-stage network, as shown in Figure 2. A
loss in the front of a gain stage decreases gain db for db and increases noise figure and
input intercept point db for db (see Fig-2). This is true for noise figure as long as
additional noise is not added from external sources in the lossy stage. It is true for
intercept point if the loss does not generate distortion products of its own (that is, it is
linear).
CASE-1
Figure-2
Now, all dB values of gain, noise figure, and input intercept points are converted to
numeric using numeric equations. Note that the last stage gain does not need to be
converted to numeric for cascaded noise figure or cascaded inter-modulation
distortion equations.
The system numeric gains are given by:
g1= 10 g2 = 3.16
The noise factor of each stage is:
F1 = 2.5 F2 = 5 F3 = 4
Finally, the numeric input intercept points at each stage are given by:
ip1 = 0.158 ip2 = 0.2 ip3 = 15.85
Gain = 10db
NF = 4db
IPi3 = -8dbm
Gain = 5db
NF = 7db
IPi3 = -7dbm
Gain = 6db
NF = 6db
IPi3 = 12dbm

3. System noise factor is given as :
FT = 2.5 + 5-1 5−1
10
+ 4−1
10 x 3.16
= 3
Converting to noise figure yield:
NFT = 10lg(3) = 4.77dB
Third order intercept point is calculated :
1
IPiT
=
1
0.158
+
10
0.2
+
10 x 3.16
15.85
= 58.32
or
IpiT = 0.017
finally;
IP3i = 10lg(0.017) = -17.7dBm
Next calculating the sensitivity using the equation :
SensitivitydBm = -174dBm + 41.44dB + 10dB = -117.46dBm
Spur-free dynamic range is calculated from equation :
SFDR = 2/3 [ 3.3dBm + 127.46dB -21dB ] = 73dB
CASE-2
If the filter is moved in front of the RF amplifier, the new combined receiver is shown in
below.
Gain = 7db
NF = 7db
IPi3 = -5dbm
Gain = 8db
NF = 4db
IPi3 = -10dbm
Gain = 6db
NF = 6db
IPi3 = 12dbm

4. Figure – 3
The new sensitivity and spur-free dynamic range are calculated similar to the above
calculations and are:
SensitivitydBm = -114.93 dBm and SFDR = 71.67dB.
Conclusion
Both the sensitivity and the SFDR where degraded by moving the RF Filter.