![]() ![]() With a suitable choice of bias, it is possible to have a stable amplifier when the input is connected to a resonant circuit, obviating the need for an isolator.Ī two-port microwave network is conveniently described by a scattering matrix relating the voltage V + incident on one port with that ( V − ) scattered from the same or a second port. In this letter, we report measurements of the full set of complex scattering (S) parameters of the MSA, and use them to demonstrate that the MSA is conditionally stable. Unless the amplifier is unconditionally stable, however, this may lead to unstable behavior and loss of amplification. A desirable alternative is to connect the amplifier directly to the measurement circuit. ![]() Isolators require a magnetic field to break time-reversal symmetry, and are often noisy, lossy and bulky. To tame the effects of a complex source impedance one typically inserts an isolator between the source and the input. In both cases, the source impedance is a complex function of frequency. In a typical application, such as axion detection 1 or dispersive qubit readout, 11 the MSA is used to measure the frequency response of a resonant cavity or circuit. With appropriate current and flux biases, the SQUD converts an input flux Φ to a voltage V with a transfer function V Φ ≡ ∂ V / ∂ Φ. At the fundamental resonance, there is substantial coupling between the magnetic field of the microstrip mode and the SQUID. A thin dielectric layer covers the washer, and a square coil deposited over it to form a microstrip resonator. 1 The MSA consists of a superconducting square washer 10 interrupted by two resistively shunted Josephson junctions. The microstrip SQUID (Superconducting quantum interference device) amplifier (MSA), 4 cooled to millikelvin temperatures, offers both a gain in excess of 25 dB and a noise temperature within a factor of two 8 of the standard quantum limit 9-typically 50 times lower than that of a high electron mobility transistor. What is it about MSG that makes it the final word on stable gain when, I'll say, the 23 or even the 26dB gain circle seems safely out of the output stability circle's unstable region and seems like there would still be some safe terminating impedances, although not many, available.A growing number of applications including a search for dark-matter axions, 1 the readout of superconducting qubits 2 and a postamplifier for the radio-frequency single electron transistor 3 require high-gain, low-noise amplifiers 4–7 at frequencies around 1 GHz. Apparently, gain seems to be infinite with respect to a potentially unstable transistor. Only when I jumped to 50 and 100dB did the gain circles just align with the output stability circle. The 29dB gain circle is dangerously close to but still outside the output stability circle's unstable region. ![]() For the heck of it, I plotted gain circles all the way up to the ludicrous values of 50 and 100dB to see what would happen. Notice that some of the 22.1dB constant-gain circle is located pretty far away and outside of the output stability circle's unstable region. I have the output stability circle plotted and the unstable region marked as UR on the Smith chart. The on-line article also said that "one should never try to tease more gain from the transistor than the MSG". For my transistor, the MSG in absolute gain 162.5 or 22.1dB as shown on the attached Smith chart. MSG is simply the ratio of the magnitude of S21 over the magnitude of S12. I recently read on-line that for a potentially unstable transistor the maximum gain that can achieved is the MSG or maximum stable gain. I was plotting constant-gain circles on the Smith chart the other day for a potentially unstable RF transistor.
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