73 lines
2.0 KiB
Python
Executable File
73 lines
2.0 KiB
Python
Executable File
#!/usr/bin/env python3
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"""
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try to understand which transfer characteristics can be used to create stable logic.
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"""
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def fwd(offset: float, amp: float):
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return lambda x: min(1.0, offset + amp*x)
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def inv(offset: float, amp: float):
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return lambda x: max(0.0, 1.0 - offset - amp*x)
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def test_stability(fwd, inv):
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low = 0.0
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high = 1.0
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mid = 0.5
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for i in range(32):
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low, high, mid = fwd(inv(high)), fwd(inv(low)), fwd(inv(mid))
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print(f"low {low:.2f} high {high:.2f} bistable {mid:.2f}")
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print("stability: 0.2 + 2.0*x")
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test_stability(fwd(0.2, 2.0), inv(0.2, 2.0))
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print("stability: 0.2 + 1.5*x")
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test_stability(fwd(0.2, 1.5), inv(0.2, 1.5))
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print("stability: 0.2 + 1.1*x")
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test_stability(fwd(0.2, 1.1), inv(0.2, 1.1))
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print("stability: 0.4 + 1.1*x")
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test_stability(fwd(0.4, 1.1), inv(0.4, 1.1))
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print("stability: 0.5 + 2.0*x")
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test_stability(fwd(0.5, 2.0), inv(0.5, 2.0))
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print("stability: 0.9*x")
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test_stability(fwd(0.0, 0.9), inv(0.0, 0.9))
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print("stability: 0.2 + 1.5*x; 0.9 - 0.7*x")
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test_stability(fwd(0.2, 1.5), inv(0.1, 0.7))
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print("stability: 0.1 + 1.3*x; 0.9 - 0.7*x")
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test_stability(fwd(0.1, 1.3), inv(0.1, 0.7))
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print("""\
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offset isn't a deal-breaker until it approaches 50%.
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for any offset < 0.5, amplification > 1.0, there is *some* stable pair of levels.
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as offset increases, the stable pairs become closer together
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""")
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def test_stability_inv(inv, mid=0.5):
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low = 0.0
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high = 1.0
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for i in range(32):
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low, high, mid = inv(high), inv(low), inv(mid)
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print(f"low {low:.2f} high {high:.2f} bistable {mid:.2f}")
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print("stability_inv: 0.2 + 2.0*x")
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test_stability_inv(inv(0.2, 2.0))
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print("stability_inv: 0.2 + 1.1*x")
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test_stability_inv(inv(0.2, 1.1))
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print("stability_inv: 0.5 + 1.1*x")
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test_stability_inv(inv(0.5, 1.1), 0.2)
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print("stability_inv: 0.7 + 1.1*x")
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test_stability_inv(inv(0.7, 1.1), 0.1)
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print("""\
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inverter-only circuits can be stable, even if they ordinarily bias to just one direction...
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the same amp > 1.0 condition holds.
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importantly, offset > 0.5 becomes *fine*
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""")
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