Figure A.15.: Output spectrum of a nonlinear device with a two-tone input
by filtering and will be a reducing factor if their magnitudes are high. In the case of the two tone singal conselation will such curruptive components be refered to as third order intermodulation products. If a mixer should be used to benefit the generation of sum and differance frequencies, must hence the additional tone be selected such that a maximum frequency sepearation is enabled (section A.9). This is also illustrated in figure A.15 where the difference frequency is greatly separated away from others components. On the other hand, can an increased waveform complexity, yield intermodulation effects. Hence must allways the signal conselation be considered agains the circuits linear properties. Typically will such passband intermodulation, come from the third-order-products, third- order intermodulation distortion. Hence can often a prehand signal analysis including the third-order-products be benificial to see the possible impacts in spectrum. A typical measured spectrum with likewise spurious components can be identified by distinct discrete peaks of the above mentioned harmonics. Dependent of the type of radar in use and what targets are desirable, spurious components can generate great confusion to the detection of real targets if not undesired components are remove.
A.9. Mixers
The section will give an introduction to mixers, how they can be utilized in a radar system and basic differences between different types. Since they are mostly made of nonlinear components like diodes and FET-transistors, they will influence the system performance as describes for nonlinear and active componentes in the Noise and Distortion section. The section has been written primarily based on [28, chap.3&7].
General
To exploit the high frequencies in the radar/RF part of the electromagnetic spectrum, baseband signals needs to be shifted up and down at the radar front-end. Often mixers are used to do this job,making them one of the key hardware components of a radar systems. A mixer is a device that uses nonlinear or time-varying elements to make waveforms
shift in the frequency domain. In general the mixer is a three-port device who makes an frequency conversionof two different frequencies. The output of a mixer is ideally the sum and difference frequencies from these two inputs. In a radar this is exploited to make the fundamental operation of up-conversion and down-conversion. Up-conversion is done in order to convert a radar signal from baseband up to a practical radio frequency(RF) for transmission and detection, often done in several steps via the use of intermediate frequencies(IF). Down conversion is done in the receiving part of an radar, by converting a RF-signal down to one or several intermediate frequencies, and back to baseband for signal prossesing of the received radar-echo. These two fundamental operations are illustrated in figure A.16, were (a) is the up-conversion and (b) is the down-conversion.
Figure A.16.: Frequency conversion by a mixer
Figure A.16 shows the idealized view of ta mixer but as mentioned i section A.8 the actual mixer outputs more harmonics than the desired ones due to the nonlinearity. The up-conversion occurs in a transmitter where a high frequency oscillator (LO) is mixed with the baseband signal or IF signal. Mathematically the up-conversion can be idealized described as vLO(t) = cos 2πfLOt vIF(t) = cos 2πfIFt ⇓ vRF(t) = KvLO(t)vIF(t) = K
2 [cos 2π(fLO− fIF)t + cos 2π(fLO+ fIF)t] (A.38) K is a constant that takes the loss between the desired component (output) and the applied component (input), into account (Conversion loss). In up-conversion this is the loss from
A.9. Mixers 183
fLO to fLO − fIF. If both side bands are utilized by the mixer, the mixer percerves a
Double side bandsignal (fLO± fIF) in respect to the carrier (fLO). On the other hand
a Down-conversion will be in a similar way but with the IF signal as output, converted down from RF. The resulting output is
vIF(t) = KvRF(t)vLO(t)
= K
2 [cos 2π(fRF − fLO)t + cos 2π(fRF + fLO)t] (A.39) As is illustrated in figure A.16 (b) the desired component in baseband is fIF = fRF−fLO,
which can be separated with low pass filtering. Totally the mixer can generate spurious componentsfor:
mfRF ± nfLO = fIF
A problem however is when the mixer is a part of the receiver in down-conversion. Since the antenna often see a wide band of frequencies, the receiver will receive two RF signals that where generated in the up-conversion (upper/lower sideband, seen in figure A.16 (a))
fRF = fLO− fIF (A.40)
fIM = fLO+ fIF (A.41)
When down-converted, these two equations is in put into fIF = fRF− fLOas fRF which
will respectively give fIF and −fIF after low pass filtering. The negative response from
fIM is known as the Image frequency. The problem is that the two responses are not
indistinguishable at the IF part of the receiver front-end. This needs to be considered because undesired spectral component can be folded over to the positive side of spectrum, masking or distorting, the target in typical digital receivers.
Another important parameter of mixers is the Conversion loss. This parameter account for resistive losses and other losses that occur in the frequency conversion prosses. In up-conversion this will be from IF to RF and in down-conversion from RF to IF. The conversion loss for down-conversion is defined as
Lc= 10log
Available RF input power
Available IF output power [dB] (A.42) As other microwave components the mixer will have internally generated noise, generated by the diodes, transistors or the resistive losses. The noise figure of the mixer will be dependent of the mixer operation mode, if it uses the full double side band or only one single side band. Typical Fn of practical mixers are in the range of 1dB to 5dB.
Generally the diode mixers achieve lower noise figures than transistor mixers. In addition mixers with nonlinearity will suffer from intermodulation. Normal values of third-order- intermodulation distortion will be in the range of 15dBm to 30dBm.
From figure A.16 it is shown a idealized picture of the resulting frequency spectrum of the mixer process, by contrast real mixers will not be able to decouple the applied signals. This will lead to leakage of power through the mixer from the oscillator. If this is not taken care of with filtering or other technics, strong signals like LO in up-conversion can be radiated by the antenna. The isolation of the input ports to the output port is therefore a important parameter.
Types of mixers
Generally two types of mixers are used, diode mixers and FET mixers. There can be several realizations of mixer types of the two main types. The different types of realizations is shown with typical values for the diode mixer approach in figure A.9 [28, p.245]. Note that there exist both active and passive mixers. More detailed descriptions of these types are given in [28, Chap.7].
Table A.1.: Summarized characteristics of several mixer realizations of diode mixers
Mixer Number of RF Input RF-LO Conversion Third-Order Type Diodes Match Isolation Loss Intercept
Single-ended 1 Poor Fair Good Fair
Balanced(90◦) 2 Good Poor Good Fair
Balanced(180◦) 2 Fair Excellent Good Fair Doubled-balanced 4 Poor Excellent Excellent Excellent Image reject 2 or 4 Good Good Good Good
The main difference between diode and FET-mixers can be observed from the typical values of single-end mixers in table A.9 [28, p.239].
Table A.2.: Difference between singel-ended diode and FET-mixers
Mixer Conversion Noise 1 dB 3rd Order Type Gain (1/Lc) Figure Compression Intercept
Diode -5dB 5 to 7dB -6 to -1 dBm 5dBm FET 6dB 7 to 8dB 5 to 6 dBm 20dBm
FET-mixers have as diode mixers, several types of designs. Typical FET configurations is the use of dual-gate FET, where the LO and RF ports are separately FET gates. As a consequence there will be a high degree of RF-LO isolation, but very high noise figure. Another typical configuration is the use of two FET transistors in parallell as an differential amplifier, together with balun-networks. This design is shown in figure A.17. An often used extended design method of the differential type, is the Gilbert cell-mixer. This is very much used in integrated circuits. It has in addition to figure A.17 two differential stages which is an double balanced mixer. Because of this it achieves high dynamic range and high isolation between all ports. Another benefit is that it cancels all even-odd intermodulation products.
A.9. Mixers 185
Figure A.17.: Differential mixer
Different FET-mixer designs for balanced and image reject mixers are shown in fig- ures A.18 and A.19 with the resulting spectrum properties for upconversion. The illustrating figures are from the NTNU lecture series of the course Integrated Microwave Circuits [43].
Power
f
IF Frequencyf
RFf
LOf
USFigure A.18.: Balanced mixer
The balanced mixer will typically suppress the carrier and the IF output. The figure above consist of two parallell mixers in a balun configuration. Here the IF, RF, LO and Image frequency are denoted fIF, fRF, fLO and fus.
Power
f
IF Frequencyf
RFf
LOf
USFigure A.19.: Image reject mixer
An image reject mixer will both suppress the carrier, the IF and the image component. This is done by two parallell balanced mixers with additional balun circuit. Note that the suppression is a very important property, since the output spectrum will overlap into another and distort the wanted signal, as shown in figure A.18 and A.19.