the short is +0.6, and the load is +0.75; thus, the difference between the open and the short moves from 2 to only 0.4. These reflections are mapped to the full Smith chart through the error correction math, in such a way that the values from the reflections, and any instability, are multiplied by 5. Also, since the load condition has a large signal in the b1 receiver, any instability in that signal is apparent as a directivity error, which is also multiplied by 5. In theory, if directivity is defined as the average of the open/short response relative to the load response, then the directivity of a 1+gamma reflectometer is about 0 dB (remember that directivity for a coupler or bridge is always positive, often 20 dB or more).
Theoretically, any directivity error can be corrected for by a calibration, but in practice, certain unstable errors can cause uncorrectable errors when the directivity is poor. Thus, 1+gamma structures have largely disappeared from use. Also, this same multiplying effect causes any slight drift in the test port cable to cause a considerable change in the measured reflection coefficient, after calibration.
2.2.5 VNA Receivers
The final RF components in a VNA block diagram are the test and reference receivers. Dynamic range is a key specification of a VNA and is sometimes referred to as the difference between the maximum signal level that the receiver can accept while still operating and the noise floor of the receiver. In most cases, the maximum damage level is significantly above the maximum operating level of the receiver, which is usually limited by the input compression level of the receiver. The maximum operating level is set by the structure of the components, but for most modern VNAs, it is around the −5 dBm at the receiver mixer input, or about +10 dBm at the test port, after considering the coupling factor of the test port coupler. The noise floor of the receiver is set primarily by the type of mixing down‐converter used, of which the two principal types are sampling down‐converters (or samplers) and mixers.
2.2.5.1 Samplers
The sampling down‐converters are circuits that are driven by a low frequency pulse, which has very high harmonic content. The example circuit shown in Figure 2.21 is typical of older VNA sampling receivers such as found in the HP8753 or HP8510 VNAs. In the circuit, the diode pair acts like a switch, which is driven with a very short pulse from a pulse generator driven by a voltage‐controlled oscillator (VCO), operating at relatively low frequencies. The short conduction angle (the amount of a cycle that the diodes conduct) of the pulse means that the frequency content is very high, sometimes referred to as a harmonic‐comb, and the sampler can convert frequencies much higher than the VCO drive.
Figure 2.21 Schematic of a sampler.
It is not unusual to use harmonics of up to 200 times the VCO frequency. Because the conduction angle is so short, the effective input impedance is high, essentially multiplied by the maximum harmonic number, and this means the effective noise figure of the sampler is high as well. Since the conduction angle does not depend upon the frequency being measured, the noise figure does not depend upon the frequency being measured. The conduction angle and conversion efficiency can be adjusted by adjusting the diode bias so that they are not quite turned on, and the pulse provided by the VCO gives the extra current to turn on the diodes fully.
Some advantages of samplers are that they do not require a high frequency local oscillator, as a mixer would, and they can simultaneously down‐convert a signal and all its harmonics to the intermediate frequency (IF). This capability is exploited in a sampling oscilloscope, and now in some of the modern versions of sampling VNAs used for non‐linear measurements. However, for the most part samplers have been largely abandoned in VNAs due to a number of difficult problems that they present.
The foremost problem is the degraded noise floor in the sampler‐based VNA. The effective noise floor is further reduced as the conversion efficiency of higher‐order harmonics typically degrades near the top of the sampler frequency range. Almost all modern VNAs use some form of mathematical response correction on the sampler response so that frequency response of the VNA receiver to a constant input power appears flat over its entire frequency range. This response correction, which removes the effect of roll‐off in real conversion loss, has the consequence of increasing the apparent noise floor of the sampler at higher frequencies.
A secondary problem with samplers is that the rich harmonic‐content of the VCO dictates that the sampling receiver has many regions where it is sensitive to other signals, such as harmonics or spurious signals of the VNA source or DUT, and spurious signals present at the DUT output. This makes sampling receivers particularly poor at measuring mixers or frequency converters, where the sampling comb‐tooth can cross mixer output signals at many different frequencies. Figure 2.22 shows an example of spurs from a source generating responses in a sampling receiver. In this case, the source signal is generated by mixing a 3.8 GHz fixed RF signal with a 3.8–6.8 GHz swept yttrium‐iron‐garnet (YIG) oscillator LO. The mixed product provides the desired 0–3 GHz source output, but spurious signals at 2 · RF − LO and 3 · RF − 2 · LO do show up in the 0–3 GHz VNA measurement receiver band. While small, these spurious responses do degrade the S21 accuracy.
Figure 2.22 Spurs from a source crossing a harmonic of the VCO.
Another difficulty with sampling mixers becomes apparent when measuring filters in the stopband and is caused by remixing signals reflected off the DUT back into the input reflection receiver such as the b1 receiver. Because this effect has the appearance of a signal bouncing off the input reflection of the filter stopband and then bouncing off the b1 mixer (at a different frequency), it is sometimes called sampler bounce (or mixer bounce in the case of mixers). Designs of these components must be carefully considered to avoid these bounce signals, and the basic design of samplers make them especially susceptible to this particular type of crosstalk.
For these reasons, and the fact that creating wideband mixers with full‐band RF‐frequency LOs has become much more cost effective, the use of samplers in VNAs has been phased out.
2.2.5.2 Mixers
Almost exclusively, modern VNAs use mixers as VNA receivers. The mixers are driven by a fundamental or low‐harmonic‐order LO. This provides a much larger conduction angle for frequency conversion and as such provides a lower noise floor. The trade‐off, of course, is the cost of the LO, which may be due to its increased complexity.
2.2.5.3 Noise Floor
With mixers used as VNA receivers, the critical performance attributes are noise floor and input compression point. A fundamental LO provides best performance; using a third‐order harmonic of the LO to obtain higher RF frequency response theoretically degrades the conversion loss by 9 dB, and fifth harmonic degrades it by 14 dB, based the idea that the LO drives the mixer into square‐wave conversion. This degradation in conversion loss is represented as an increase in noise floor for most VNAs, due to the internal factory‐based response correction.
2.2.5.4 Spurious Responses
Mixers have
