EEEB273 – Electronics Analysis & Design II Learning Outcome (4) Able to: • Analyze and design a basic two-transistor MOSFET current-source circuit with additional MOSFET devices in the reference portion of MOSFET the circuit to obtain a given bias current. • Analyze and design more sophisticated Current MOSFET current-source circuits, such as the cascode circuit, Wilson circuit, and wide-swing cascode circuit. Sources • Analyze the output resistance of the various MOSFET current-source circuits and design a MOSFET current- source circuit to obtain a specified output resistance. 1 2 Reference: Neamen, Chapter 10 4.0) FET Integrated Circuit Biasing 4.1) Basic Two-Transistor MOSFET Current Source • Field-effect transistor (FET) ICs are biased with 4.1.0) The Circuit current sources in the same way as bipolar circuits. Problem-Solving Technique • Analyze the reference side of the circuit to determine gate-to-source voltages. Using these gate-to-source voltages, determine the bias current in terms of the Figure 10.2: Basic reference current. two-transistor BJT • To find the output resistance, place a test voltage at the current source. output node and analyze the small-signal equivalent circuit. Keep in mind that the reference current is constant, which Fig 10.16: Basic two- may make some of the gate voltages constant or at ac transistor N-MOSFET ground. 3 current source 4 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.1) Current Relationship 4.1.1) Current Relationship (Cont) 2 • M1 is always • When = 0: IREF = Kn1(VGS −VTN1 ) (10.40) biased in saturation I region because the Therefore: REF (10.41) VGS = VTN1 + drain and gate Kn1 terminals of • M2 is always be biased in saturation region. Thus enhancement-mode 2 Load current is: I = K V −V (10.42) M1 are connected. O n2 ( GS TN 2 ) 2 Fig 10.16: Basic two- » I REF transistor N-MOSFET I = K … +V −V (10.43) O n2 K TN1 TN 2 current source. 5 n1 6 Lecturer: Dr Jamaludin Bin Omar 4-1 EEEB273 – Electronics Analysis & Design II 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.1) Current Relationship (Cont) 4.1.1) Current Relationship (Cont) • If M1 and M2 are identical transistors, then • The relationship between IO and IREF changes V = V if the width-to-length ratios, or aspect ratios, of TN1 TN 2 the 2 transistors change. and • If the transistors are matched except for the Kn1 = Kn2 aspect ratios, then Thus, I = I (10.44) O REF (W / L) I = 2 I (10.45) • Since there is NO GATE CURRENT in O (W / L) REF MOSFETS, the induced load current is identical to 1 the reference current, provided the two • This provides designers versatility in their transistors are matched. circuit designs. 7 8 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.2) Output Resistance, ro 4.1.2) Output Resistance, ro (Cont) • Stability of IO as a function of VDS is an important • Since transistors in the current mirror are consideration in many applications. processed on the same IC, all physical • Taking into account the finite output resistance parameters, such as VTN, µn, Cox, and , are of both transistors, i.e. 0: essentially identical for both devices. • Therefore, taking ratio of I to I will 2 O REF IO = Kn2 (VGS −VTN 2 ) (1+ λ2VDS 2 ) (10.46(a)) produce IO (W / L)2 (1+ λVDS 2 ) and = ⋅ (10.47) 2 (10.46(b)) I REF (W / L)1 (1+ λVDS1 ) I REF = Kn1(VGS −VTN1 ) (1+ λ1VDS1 ) which is a function of aspect ratios, , and . 9 VDS 10 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.2) Output Resistance, ro (Cont) 4.1.2) Output Resistance, ro (Cont) • The stability of can be described in terms IO As with BJT current-sources of the output resistance. • For a given IREF, VDS1 = VGS1 = constant. circuits, MOSFET current • Normally, VDS1 = VGS1 << 1, and if (W/L)2 = sources require a large , then the change in bias current with (W/L)1 output resistance for respect to a change in VDS2 is excellent stability. 1 dI 1 ≡ O ≅ λI = O (10.48) RO dVDS 2 rO2 where rO2 is the output resistance of M2 11 12 Lecturer: Dr Jamaludin Bin Omar 4-2 EEEB273 – Electronics Analysis & Design II 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.3) Reference Current, IREF 4.1.3) Reference Current, IREF (Cont) • In BJT circuits, the IREF is generally established by the bias voltages and a resistor. • Since MOSFETs can be configured to act like a resistor, the IREF in MOSFET current mirrors is usually established by using Fig 10.16: Basic two- additional transistors, e.g. M3. transistor N-MOSFET 13 Fig 10.17: MOSFET current source. 14 current source Fig 10.17: MOSFET current source. 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.3) Reference Current, IREF (Cont) 4.1.3) Reference Current, IREF (Cont) • Use current mirror in Figure 10.17 • From the circuit, can be seen: • Transistors M1 and M3 are in series. + − Assuming = 0: VGS1 +VGS3 = V −V 2 2 IREF = Kn1(VGS1 −VTN1 ) = Kn3(VGS3 −VTN 3 ) • Therefore, (W / L)3 (W / L)3 • Assuming VTN, µn, and Cox are identical in all 1− W / L transistors, thus: (W / L)1 + − ( )1 VGS1 = ⋅(V −V )+ ⋅VTN = VGS 2 W / L ( )3 (W / L)3 1+ 1+ (W / L)3 (W / L)3 (W / L) W / L V = ⋅V + 1− ⋅V 1 ( )1 GS1 (W / L) GS3 (W / L) TN 1 1 15 16 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.3) Reference Current, IREF (Cont) 4.1.3) Reference Current, IREF (Cont) • Finally, the load current, for = 0, is given by Design Example 10.8 W 1 2 I = µ C (V −V ) Objective: Design a MOSFET current source to O n ox GS 2 TN meet a set of specifications. L 2 2 ' Specifications: The circuit to be designed has the k W 2 I = n ⋅ (V −V ) (10.53) configuration shown in Figure 10.17. O 2 L GS 2 TN The bias voltages are V + = +2.5 V, V -- = 0 V. 2 ’ Transistors are available with parameters k n = 100 2 • Since the designer has control over the µA /V , VTN = 0.4 V, and = 0. width-to-length ratios of the transistors, Design the circuit such that IREF = 100 µA, IO = 60 there is a considerable flexibility in the design µA, and VDS2(sat) = 0.4 V. of MOSFET current sources. 17 18 Lecturer: Dr Jamaludin Bin Omar 4-3 EEEB273 – Electronics Analysis & Design II 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.3) Reference Current, IREF (Cont) 4.1.3) Reference Current, IREF (Cont) Design Example 10.8 (Cont) Design Example 10.8 (Cont) Solution: With VDS2(sat) = 0.4 = VGS2 – 0.4, The reference current is given by then V = 0.4 + 0.4 = 0.8 V = V ' GS2 GS1 k W 2 I = n ⋅ (V −V ) REF GS1 TN W I 2 L 1 Therefore, = O ' W I L 2 kn 2 Since V = V REF V −V GS1 GS2 = ' ( GS 2 TN ) k 2 2 L 1 n (VGS2 −VTN ) W 60 2 ∴ = = 7.5 W 100 100 2 L 2 ∴ = = 12.5 (0.8 − 0.4) L 100 2 2 1 (0.8 − 0.4) 19 2 20 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1) Basic Two-Transistor MOSFET Current Source (Cont) 4.1.3) Reference Current, IREF (Cont) 4.1.4) Using N-MOSFET and P-MOSFET Design Example 10.8 (Cont) The value of VGS3 is + -- VGS3 = (V – V ) – VGS1 = 2.5 – 0.8 = 1.7 V 2 Since IREF = Kn3 (VGS3 – VTN) , therefore W I REF = ' L k 2 3 n (V −V ) 2 GS3 TN W 100 ∴ = = 1.18 L 100 2 3 (1.7 − 0.4) 2 21 Figure 10.17 Figure P10.52 22 4.2) Multi-MOSFET Current-Source Circuits 4.2.1) Cascode Current Mirror • Among multi-MOSFET current- • As in Figure 10.18, source circuits are: with increased output resistance RO Cascode Current Mirror • IREF is established Wilson Current Mirror using another transistor. Wide-Swing Current Mirror • When all transistors are matched: Fig 10.18: MOSFET IO = IREF 23 cascode current mirror. 24 Lecturer: Dr Jamaludin Bin Omar 4-4 EEEB273 – Electronics Analysis & Design II 4.2.1) Cascode Current Mirror (Cont) 4.2.1) Cascode Current Mirror (Cont) • To determine output resistance at the drain of M4, use the small-signal equivalent circuit. • IREF constant gate voltages to M1 and M3, and hence M2 and M4, are constant Equivalent to an ac short circuit. • Therefore, the ac equivalent circuit for calculating the output resistance is shown in Figure 10.19(a). The small signal equivalent circuit is given in Figure 10.19(b). • The small-signal resistance looking Fig 10.19: Equivalent circuits of the MOSFET into the drain of M2 is rO2. 25 cascode current mirror for determining RO 26 4.2.1) Cascode Current Mirror (Cont) 4.2.1) Cascode Current Mirror (Cont) V − (−V ) • From Figure 10.19(b), summing currents at output I = I + I I = g V + x gs4 node yields x 1 2 x m gs4 V − (−V ) ro4 x gs4 I x = gmVgs4 + ro4 Also Vgs4 = −I xro2 ro2 Vx Therefore I x + I x + gmro2 I x = ro4 ro4 Vx 0 −Vgs4 − I xro2 = 0 Finally R = = r + r (1+ g r ) (10.57) O I o4 o2 m o4 x Vgs4 = −I xro2 27 28 4.2.1) Cascode Current Mirror (Cont) 4.2.1) Cascode Current Mirror (Cont) Example 10.9 • Normally gmro4 >> 1 gmro4ro2 >> ro4 Thus R ≅ g r r Objective: Compare the output resistance of the O m o4 o2 cascode MOSFET current mirror (CMCM) to that of the two-transistor MOSFET current mirror (2TMCM).