FT8 is digital communication protocol used in amateur radio bands, most prominently from 7 to 70 MHz. It's use is rising in popularity due to its reliability in weak-signal conditions, low bandwidth, and simplicity. A minimum amount of hardware is needed to get an FT8 transceiver working, and this makes it appealing to application such as military and maritime usage.
FT8 relies on a primarily digitally-driven architecture due to it's modulation scheme; 8-GFSK. However, due to its robust technical specification, a strong analog front-end is needed for successful operation.
[image of frontend] [caption]
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Proper characterization of the PDK devices is paramount for accurate circuit design in future steps. Once values such as $g_{m}$ and $V_{TH}$ are obtained, processes like gm/Id design can be utilized to derive circuit topologies and values.
nfet_01v8[image of circuit]
Start by placing a sky130_fd_pr__nfet_01v8 device with the default parameter values into a new schematic in Xschem. Attach a voltage source V1 to the gate and another V2 to the drain. Ensure that the bulk and source are grounded. Also ensure that V2 or $V_{DS}$ is held at $V_{DD}/2$ or 0.9V. Create a new code block and run a dc sweep of V1.
.control dc V1 0 3 0.01 % dc sweep of Vgs plot -i(V2) % plot drain current .endc .saveall
Once the simulation has finished, run plot -i(v2) to view the drain current vs. $V_{GS}$ graph. This graph helps to give us the transconductance $g_m$ of the MOSFET, which indicates how efficiently the device can convert a voltage to a current. To derive this value from the simulation, you can either run the command print @m.xm1.msky130_fd_pr__nfet_01v8[gm] or use the typical analytical expression: $$g_{m} \ = \ \frac{\partial{I_D}}{\partial{}V_{GS}} \ = \ \mu_{n}C_{OX}\frac{W}{L}(V_{GS}-V_{TH}) \ = \ \frac{2I_D}{V_{GS}-V_{TH}}$$
To find the threshold voltage $V_{TH}$ of the device, you can simply run the same command as above for the parameter: print @m.xm1.msky130_fd_pr__nfet_01v8[vth]
[image of circuit] Using the same circuit as before, sweep V2 instead of V1 at varying V1 values. This aids in finding the saturation point for a given $V_{GS}$ and the behavior of $I_D$ beyond $V_{DSAT}$. The code for this may look like this:
.control alter @V1[value] = 0.7 % start at Vth dc V2 0 5 0.01 plot -i(v2) alter @V1[value] = 1 % step to new Vgs value ... % continue changing Vgs alter @V1[value] = 3 dc V2 0 5 0.01 plot -i(v2) .endc .saveall
For a given DC sweep, one can obtain the $V_{DSAT}$ value by running print @m.xm1.msky130_fd_pr__nfet_01v8[vdsat]. Or, use the expression $V_{DSAT}=V_{GS}-V_{TH}$. Now that the key values of the device have been extracted, one can now determine some other Figures of Merit, such as on resistance: $$R_{on} \ = \ [\mu_{n}C_{OX}\frac{W}{L}(V_{GS}-V_{TH})]^{-1}$$ And to determine the behavior of drain current past saturation: $$\int_0^LI_D\mathrm dx \ = \ \mu_{n}C_{OX}\int_0^{V_{GS}-V_{TH}}[V_{GS}-V_{TH}-V(x)]\mathrm dV$$
$$ \therefore \ \ I_D \ = \ \frac{1}{2}\mu_nC_{OX}\frac{W}{L}(V_{GS}-V_{TH})^2(1+\lambda V_{DS}) \ \ \ \forall \ V_{DS}>V_{DSAT} $$
This concludes the basic characterization of the nfet_01v8 device. In order to obtain accurate circuit simulations and successful circuit design, one should characterize every device they intend to use from the PDK.
Typical FT8 recievers should be able to successfuly decode a received signal at atleast -80dBm with an SNR as low as -21dB. In order to conform to these specifications, a strong, simulation-proven architecture will be needed. The basic architecture of the RF front end was known from the start; a filter following the antenna to pass the target band of 7-70 MHz, followed by a low-noise amplifier and ADC.
[image of matlab architecture]
Different topologies of bandpass filters were simulated to meet specification. The final decision was a 4th order Butterworth LC bandpass. This allowed for minimum insertion loss, nominal phase delay, and a relatively low noise figure. The generalized transfer function for it's frequency response has been provided below.
$$ | \ H(j\omega) \ | = [1+(\frac{\omega}{\omega_{c}})^{2n}]^{-1/2} $$
The intrinsic attenuation can be calculated aswell.
$$ A_{d} = 10\log_{10}(1+(\frac{\omega}{\omega_{c}})^{2n}) $$
[image of matlab architecture]