Chapter-5-Current-Mirrors

When Vin1-Vin2=0, Maximum current ID1=ID2= ID3=ID4, and hence maximum small-signal gain;
When Vin1-Vin2>0, ID2, M4 enter triode region, the gain decrease;
Largely reduce the change so that VY is more close to VX, and hence Iout more closely track IREF.
Current Mirrors
Cascode current mirrors (2)
More accurate but at cost of higher voltage headroom:
Current Mirrors
Cascode current mirrors (4)
In order to solve the trade-off between accuracy and voltage headroom:
Minimum allowable VP becomes:
(VGS3 VTH ) (VGS4 VTH )
Rout [1/ gm1 gm2ro2 (1/ gm1) ro2 ] || ro4 (1/ gm1 2ro2 ) || ro4 {if symmetry, gm1 gm2} (2ro2 ) || ro4 {if ro2 1/ gm1}
| Av | Gm Rout

பைடு நூலகம்g m1 2
Small-signal analysis:
Differential input and single-ended output, amplitude of Vx and Vy are not same, cannot use the concept of half circuit to analysis.
Minimum allowable voltage at node P is equal to:.
VN VTH VGS0 VGS1 VTH (VGS0 VTH ) (VGS1 VTH ) VTH
One Vgs higher than basic current mirror:.
gm2
ro2
{if ignore body effect}
Then:
1 ro4
VP
Req

ro 2
Vin
Req

1 g m1
2 ro4 ro 2
Current Mirrors
Active current mirrors (4)
Second approach to calculate |Av|:
Less one VTH, So this can be used in low-voltage application.
Current Mirrors
Active current mirrors (1)
How about if we use a current mirror as load of a differential pair?
Please understand the first approach by your self (p151-152) Here I only introduce the second method.
Current Mirrors
Differential pair with Active current mirrors (7)
Use Thevenin equivalent to calculate gain of the circuit:
Current Mirrors
Differential pair with Active current mirrors (8)
Take point P as Virtual Ground, use half-circuit concept to calculate the Thevenin equivalent voltage:
I x1
Vout Veq Req RM 3,drain
Vout g r V m1,2 o1,2 in
2ro1,2

1 gm3
||
ro3
{RM 3,drain refer to p53}
If the current flows through 1/gm3 is mirrored into M4 with unity gain:
Refer to eq. (3.104), page 79:
Vout Vp

gm2ro2 1 ro2 ro4
ro
4
gm2ro2 1 1 ro2 ro 4
gm2ro2 1 ro2 ro 4
{if gm2ro2 1}
Current Mirrors
Active current mirrors (5)
I x1 I x1
ro3 ro3 1/ gm3
Vout ro 4
!! A little different from text book
Current Mirrors
Differential pair with Active current mirrors (10)
And:
Vout g r V m1,2 o1,2 in (1
Current Mirrors
Cascode current mirrors (3)
M2 enter triode region M3 enter triode region
VX When VX drops from high voltage to low voltage, M3 enter triode region first, and then M2:.
ro3,4
) Vout
2ro1,2

1 gm3,4
||
ro3,4
ro3,4 1/ gm3,4
ro3,4
Assuming 2ro1,2>>(1/gm3,4)||ro3,4 and ro3,4>>1/gm3,4, we obtain:
Second approach to calculate |Av|:
Vout Vout VP Vin Vp Vin
1 ro4

ro2 gm2ro2
2 ro4 1 ro2
ro 2
ro 4
gm2ro2ro4 2ro2 ro4

gm2 2
[(2ro2 ) || ro4 ]
Current Mirrors
| Av | Gm Rout
Gm Iout /Vin (g V m1 in / 2) /Vin gm1 / 2
Current Mirrors
Active current mirrors (2)
Rout is equal to the output resistance of a CS with a degeneration resistance of 1/gm1.
Large-signal analysis:
If Vin1-Vin2=-, M1, M3, M4 off, ID4=0, M5 and M2 are in deep triode region, Vout=0;
When (Vin1-Vin2), ID1=ID3=ID4 , Vout ;
Current Mirrors
Cascode current mirrors (1)
Use cascode to get more accurate current:
VY VP / (gm3 gmb3)ro3 Refer to P65 Figure 3.23 and eq. (3.63)
Veq g r V m1,2 o1,2 in
While the equivalent impedance is:
Req ro1 ro2 2ro1,2
Current Mirrors
Differential pair with Active current mirrors (9)
Then:
Always biased in the condition of Vin1=Vin2, so that the gain of differential pair with active current mirrors keeps largest.
Current Mirrors
Differential pair with Active current mirrors (5)
[(
2ro
2
)
||
ro4 ]
Current Mirrors
Active current mirrors (3)
Second approach to calculate |Av|:
Refer to eq. (3.110), page 80:
Req

1 gm2

ro 4 g m 2 ro 2
1 (1 ro4 )
Basic current mirrors (2)
For example:
If consider channel-length modulation: VX=VGS0=VGST , while VP is dependent on the CM level and input signal of M1 and M2 and may not equal VX. In this case, IT not track IREF accurately
Current Mirrors
Differential pair with Active current mirrors (6)
There two approaches to calculate gain of the circuit: One is to use the concept of Gm and Rout; The second is to use Thevenin equivalent.
Current Mirrors
Differential pair with Active current mirrors (2)
Large-signal analysis:
Current Mirrors
Differential pair with Active current mirrors (3)
Fig. 5.5 Basic current mirror
Diode-connected to ensure M1 always in saturation! If not consider channel-length modulation:
I out

(W (W
/ L)2 / L)1
I REF
Current Mirrors
When Vin1-Vin2=, M2 off and ID2=0, M4 in deep triode region, Vout=VDD.
Current Mirrors
Differential pair with Active current mirrors (4)
Large-signal analysis result:
Current Mirrors (电流镜）
Basic current mirrors (1)
As we seen, current sources are frequently used in analog circuit.
How can we supply an accurate ISS? If we have an accurate current source reference, we can copy it to the circuit.
Differential pair with Active current mirrors (1)
Problem of above differential pair: Small-signal drain current of M1 is “wasted”
Solve method: Use differential pair with active current mirror to combine the small-signal current together.