scripts: document the conditions which lead to "stable" logic levels

crates/post/scripts/levels_proto.py

@@ -0,0 +1,72 @@
+#!/usr/bin/env python3
+"""
+try to understand which transfer characteristics can be used to create stable logic.
+"""
+
+def fwd(offset: float, amp: float):
+    return lambda x: min(1.0, offset + amp*x)
+
+def inv(offset: float, amp: float):
+    return lambda x: max(0.0, 1.0 - offset - amp*x)
+
+def test_stability(fwd, inv):
+    low = 0.0
+    high = 1.0
+    mid = 0.5
+    for i in range(32):
+        low, high, mid = fwd(inv(high)), fwd(inv(low)), fwd(inv(mid))
+        print(f"low {low:.2f} high {high:.2f} bistable {mid:.2f}")
+
+print("stability: 0.2 + 2.0*x")
+test_stability(fwd(0.2, 2.0), inv(0.2, 2.0))
+
+print("stability: 0.2 + 1.5*x")
+test_stability(fwd(0.2, 1.5), inv(0.2, 1.5))
+
+print("stability: 0.2 + 1.1*x")
+test_stability(fwd(0.2, 1.1), inv(0.2, 1.1))
+
+print("stability: 0.4 + 1.1*x")
+test_stability(fwd(0.4, 1.1), inv(0.4, 1.1))
+
+print("stability: 0.5 + 2.0*x")
+test_stability(fwd(0.5, 2.0), inv(0.5, 2.0))
+
+print("stability: 0.9*x")
+test_stability(fwd(0.0, 0.9), inv(0.0, 0.9))
+
+print("stability: 0.2 + 1.5*x; 0.9 - 0.7*x")
+test_stability(fwd(0.2, 1.5), inv(0.1, 0.7))
+print("stability: 0.1 + 1.3*x; 0.9 - 0.7*x")
+test_stability(fwd(0.1, 1.3), inv(0.1, 0.7))
+
+print("""\
+    offset isn't a deal-breaker until it approaches 50%.
+    for any offset < 0.5, amplification > 1.0, there is *some* stable pair of levels.
+    as offset increases, the stable pairs become closer together
+""")
+
+def test_stability_inv(inv, mid=0.5):
+    low = 0.0
+    high = 1.0
+    for i in range(32):
+        low, high, mid = inv(high), inv(low), inv(mid)
+        print(f"low {low:.2f} high {high:.2f} bistable {mid:.2f}")
+
+print("stability_inv: 0.2 + 2.0*x")
+test_stability_inv(inv(0.2, 2.0))
+
+print("stability_inv: 0.2 + 1.1*x")
+test_stability_inv(inv(0.2, 1.1))
+
+print("stability_inv: 0.5 + 1.1*x")
+test_stability_inv(inv(0.5, 1.1), 0.2)
+
+print("stability_inv: 0.7 + 1.1*x")
+test_stability_inv(inv(0.7, 1.1), 0.1)
+
+print("""\
+    inverter-only circuits can be stable, even if they ordinarily bias to just one direction...
+    the same amp > 1.0 condition holds.
+    importantly, offset > 0.5 becomes *fine*
+""")