Most of the receiver design efforts of the past twenty years have been directed toward replacing already proven vacuum tube technologies with newly developed semiconductors. This was initially considered an easy task, but the results have been surprisingly poor. While such characteristics as high sensitivity and good selectivity were maintained; the new solid-state designs lacked dynamic range.
In an increasingly dense rf spectrum, the concept behind good dynamic range performance for a communication receiver extends to more than the ability to detect very weak signals in the presence of strong signals which may be greater in amplitude by as much as 100 dB. This concept should also include a high degree of rejection to spurious products produced by non linear interaction of many powerful signals, sometimes far removed from the receiving frequency. Let's first define dynamic range.
Dynamic range is the power range over which a device such as a radio receiver provides useful operation. The upper limit of the dynamic range (P) is limited by the level of two equal input signals creating a third-order intermodulation product at the output of the receiver, which is equal in amplitude to the minimum detectable signal (MDS) level. The MDS (some times referred to as the noise floor) is considered as the lower limit ( P L ) of the dynamic range, and is defined as a signal 3 dB greater than the equivalent noise level for a specified i-f bandwidth. The minimum detectable signal can be found by using equation 12-1.
Puate = MDS(dBm) = -171 dBm* + NF(dB) + 10 log i-f - BW (Hz)
Eq. 1
Where: MDS is lower power limit of dynamic range in dBm.
NF is System noise figure in dB i-f-BW is i-f Bandwidth in Hz
[•KTB + 3 dB = -174 4-3 = -171 dBm ]
P is lower power limit of dynamic range in dBm.
The upper limit of the dynamic range can then be expressed by using equation 2.
P umin = 1/3 (MDS + 2 IP) (Eq. 2 )
=1/3 (-171 (dBm) + NF (dB) + 10 LOG i-f-BW (Hz) ) + 2/3 IP (dBm)
Where: Pu is the upper power limit of the dynamic range in dBm IP is Receiver's third order input intercept point in dBm.
By combining the two equations, we can find equation 3 for the total spurious-free dynamic range:
SFDR (dBm) = P u (dBm) - P1 (dBm)
= 1/3 (MDS + 2 IP) - MDS = 2/3 (IP - MDS)
= 2/3 (IP (dBm) - NF (dB) - 10 Log i-f-BW (Hz) + 171 (dBm)
Where: SFDR is the spurious free dynamic range.
Eq. 3
It can be seen from this equation that the dynamic range is directly proportional to the intercept point (IP) and inversely proportional to the noise figure (NF), and i-f bandwidth (i-f-BW). We can then say that the dynamic range improves with the lowest noise figures, narrower i-f bandwidths and higher intercept points.
The following example shows a practical application for the dynamic range formula. Assume a typical high performance receiver with a noise figure of 8 dB, an i-f bandwidth of 2.1 kHz and an input intercept point of +20 dBm. Substituting these quantities in equation 3 yields; SFDR = 2/3 (+20 dBm - 8 dB - 10 log 2100 Hz + 171 dBm) = 99.85 dB.
••• SFDR = 99.85 dB.
Fig. 1. Determining the dynamic range of a receiver with a noise
figure of 8 dB, an i-f bandwidth of 2.1 kHz and an input intercept point
of +20 dBm.
The total distribution of this number can best be understood by examining the graph in Fig. 1. We know that the total spurious-free dynamic range (SFDR) for our receiver is 99.85 dB, but what is not known is where does this range fit in the total picture of the receiver's sensitivity and once this is found, what does this range mean from a practical performance point of view. We had previously determined that the lower limit of the dynamic range is given by the minimum detectable signal (MDS). If using equation 1 for our example, we find the lower limit of the receiver's dynamic range to be -129.7 dBm.
MDS = -171 + 8 + 10 Log 2100 = -129.77
We can then say that the system's noise figure for an i-f bandwidth of 2.1 kHz is 3 dB below this number, or -132.7 dBm (MDS is defined as a signal 3 dB greater than the equivalent noise level for a specified i-f bandwidth). Knowing the MDS, the IP (20 dBm) and with the help of equation 2, we can determine the upper limit of our 99.85 dB dynamic range.
P u = 1/3 (-129.77 + 40) = -29.92 dBm.
The same result would be obtained if we added the total dynamic range of 99.85 dB to the MDS. P u = 99.85 + (-129.77) = -29.92 dBm.
This last procedure could be used to verify the validity of equation 2.
If these numbers are plotted as shown in Fig. 1, we can conclude that the receiver in our example will perform undisturbed for all input signals varying from approximately -30 dBm to -130 dBm, with the receiver tuned to a third-order intermodulation product produced by two strong signals equal in amplitude and different in frequency from each other. The amplitude of these signals as well as their difference frequency (IF) were represented in our example by the +20 dBm input intercept point. In practice, this quantity is a function of the output intercept of all non-linear elements, such as mixers, amplifiers, etc., involved in the design of the receiver, as we will see below.
Fig. 2. Determining output and input intercepts for a radio receiver.
Fig. 3. Measurement of MDS.
Fig. 4. Measurement of output intercept point. Input intercept can
then be plotted and used in the dynamic range formula.
Fig. 5. The WJ-8617A is a high-dynamic-range vhf/uhf receiver, covering
the frequency range of 20 to 1100 MHz under the control of a Motorola
6800 microprocessor which makes intelligent decisions based on the characteristics
of the received signal. The receiver has a typical third order intercept
point of - 5 dBm, and a noise figure of 10 dB (courtesy of Watkins-Johnson
Company).
INTERCEPT METHOD
Fig. 2 shows the intercept method, used as an evaluation method for the strong-signal handling capability of a radio receiver. In practice, the dynamic range of a receiver is measured with the setup shown in Figs. 3 and 4. First, the minimum detectable signal (MDS) is found as shown at 3.
The MDS is measured as the power necessary to generator G expressed in dB, to produce a 3 dB increase in audio output over the noise level of the receiver as indicated by the audio voltmeter. The MDS is specified for a given i-f bandwidth and is lowest with narrowest bandwidth available. The highest bandwidth should be used for a worst case analysis.
Knowing the MDS, the setup in Fig. 4 can be used to actually find the output intercept, and with this information the input intercept can be plotted as shown in Fig. 2.
In order to find the output intercept point the outputs of the two signal generators (G1 and G) are combined in a hybrid combiner. The output of the combiner which now contains a two-tone signal is applied through a calibrated step attenuator to the receiver.
The two generators are usually 10 kHz apart with the receiver tuned to 2F2-F1 or 2F1-F2' a third order product. The attenuator is then varied until the response of the receiver at the frequency of the third-order product is the same as that produced by the MDS found earlier. The performance is specified by measuring and plotting the output intercept as shown.
If the receiver is well designed (Fig. 5), the desired output signal and the distortion product curve will intersect as high as possible, as shown in our example. This is the output intercept which describes the intermodulation response of the receiver. The input intercept can also be plotted from the intercept point as shown. This number can then be used to find the spurious free dynamic range as we previously discussed.
In conclusion, the receiver processes a weak signal in the presence of an adjacent strong signal. Because of deficiencies in the design of the first mixer and the front end, if a preamplifier is used, the receiver may not be able to copy the weak signal and it may be completely blocked out. The receiver's ability to perform under such conditions is expressed by the spurious free dynamic range. Recognizing this impediment came from military applications which required a receiver to perform properly in the presence of a number of high power transmitters broadcasting on many adjacent frequencies.