This paper presents a full duplex radio design using signal inversion and adaptive cancellation. Signal inversion uses a simple design based on a balanced/unbalanced (Balun) transformer. This new design, unlike prior work, supports wideband and high power systems. In theory, this new design has no limitation on bandwidth or power. In practice, we find that the signal inversion technique alone can cancel at least 45dB across a 40MHz bandwidth. Further, combining signal inversion cancellation with cancellation in the digital domain can reduce self-interference by up to 73dB for a 10MHz OFDM signal. This paper also presents a full duplex medium access control (MAC) design and evaluates it using a testbed of 5 prototype full duplex nodes. Full duplex reduces packet losses due to hidden terminals by up to 88%. Full duplex also mitigates unfair channel allocation in AP-based networks, increasing fairness from 0.85 to 0.98 while improving downlink throughput by 110% and uplink throughput by 15%. These experimental results show that a redesign of the wireless network stack to exploit full duplex capability can result in significant improvements in network performance.