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High external noise levels at HF and VHF allow simple, poorly-matched antennas to achieve the best possible (external-noise dominated) sensitivity. However, the large fractional bandwidths of these systems leaves them extremely susceptible to non-linear effects from strong in-band signals, resulting in a trade-off between sensitivity and linearity. We review some existing designs and consider if modifications to the front end electronics may result in greater overall performance. We demonstrate three designs representing the range of possibilities.