Current Amplifiers

1.  Introduction

  Amplifiers that are driven by a current at the input and deliver a current to the output are called current amplifiers. The ideal model of a current amplifier is shown in Fig.1.a. It is about a current controlled source having zero input equivalent resistance and infinite output resistance.

Fig.1 a) Symbol of an ideal current amplifier

  b) Symbol of a real current amplifier

  Real current amplifiers have a small input equivalent resistance and a very large output resistance, as it shown in Fig.1.b.

The structure of many integrated amplifiers is relying on simple or more complex current mirrors. To understand the operation of a current mirror it is useful to discuss first how a current source can be obtained by using transistors.

2.  Current sources

The  I-V  characteristic of an ideal current source is shown in Fig.2.a.

On the other hand the I-V output characteristic of a MOS transistor is shown in Fig.2.b. As we can see, the I-V output characteristic of the transistor, for V>V_ain, approximates the characteristic of a current source. Thus, we can conclude that a properly biased transistor behaves as a real current source at the output terminals. The inverse slope of the characteristic in fig.2.b, for V>V_min, represents the equivalent output resistance  r_o of the current source. The question now that arises is how can we bias the transistor in order to operate as a current source of a specific current value. For this purpose, the most widely used technique is the ``current mirroring technique`` . Current mirrors represent a family of many circuits each one of which has specific characteristics.For further discussion there is a number of references.[1],[2]

3.  Current mirror

 The classical way of biassing a transistor is by using a voltage divider as it is shown in Fig.3.a.

Fig.3  a) Bias through a voltage divider

          b) Bias by using a diode transistor

In the topology of Fig.3.a the resistor R₂ can be replaced by a diode transistor, as it is shown in Fig.3.b. The new topology is more preferable, for practical reasons, than the topology in Fig.3.a. In addition, it introduces a different method for biassing a transistor since, as it will be shown, for equal transistors M₁ and M₂ the drain currents at both transistors are almost equal. Hence, we can consider that the drain current at one transistor is the mirror image of the current at the other transistor. Consequently, we can say that the circuit in Fig.3.b represents as a current mirror.

  Current mirroring techniques, which apply as well in bipolar technology, are extensively used for the design of analog circuits. They simplify the circuit design, especially when multiple mirrors are used and offer a considerable flexibility in the design.

The transistors M₁ and M₂, in the circuit in Fig.4.b have a common voltage V_GS. Thus, the drain current is defined by,

Ignoring the channel length modulation, (λ=0), it results that,

or,         

     Consequently, for equal dimension transistors the currents at both transistors are almost equal. In addition, multiple copies of a current can be taken by different dimension transistors. Thus, the geometry of the transistors defines the mirror ratio. The geometry of the transistors is the unique design parameter in IC circuit design.

The discussion above is an approximation study of the real operation of a mirror. In practice, channel modulation effects considerably the currents in the branches of a mirror, as it is shown the simulation results shown in Fig.5.

Fig.5  The currents at the two transistors in the mirror in Fig.4.b

To overcome the various defects of the simple current mirror a number of improved circuits appear in the literature.[3] The simplest modification is achieved by adding a feedback source resistor in the transistor M₁, as it is shown in Fig.6.a

Fig.6  High output resistance current mirror

4.  Current mirrors as current amplifiers

  Current mirrors can be used as current amplifiers in a variaty of applications [4].

In most of the applications current amplifiers operate as low gain amplifiers without overall feedback. The frequency bandwidth of current amplifies is much higher than that of voltage amplifiers and of the order of the f_T of the transistors used. The bandwidth is almost independent of the gain of the amplifier. In addition current amplifiers are very simple in structure and can be implemented as integrated circuits in CMOS or BJT technology. 

A Current amplifier based on a simple current mirror

In Fig.7.a the topology of a current amplifier is shown which is based on a current mirror (CM). In Fig.7.b the circuit of a current amplifier is shown which is based on the simple current mirror we have studied already. To simplify the study of the circuit, the bias of both transistors is achieved through the fixed value current sources I₁ and I₂.

  a)                                                   b)

Fig.7 a) A topology of a current amplifier based on a current mirror

For the circuit in Fig.7.b it is,

 

If  k is the mirror ratio, then,

and,

Since I₁ and I₂ are ideal current sources,

Consequently, 

Thus the output current is a multiple of the input current. Hence the circuit in Fig.7.b is an inverting current amplifier. The current amplifier in Fig.7.b can be used as a DC amplifier as well. 

 The ac equivalent circuit of the amplifier is shown in Fig.8.

Fig.8  AC equivalent circuit of the amplifier in Fig.7.b

For the circuit in Fig.8 it is,

or,  

Accordingly,

That is, the equivalent input resistance of the amplifier is inversely proportional of the transconductance of M₂. Hence R_in depends on the bias current of M₂. As higher the bias currents as lower is the input resistance.

The output current is,

or,

   

The expression above is in agreement with the results we found before.

The equivalent output resistsnce is,

As lower the bias current of M₁ as higher is the output resistance.

  The maximum value of the input current i_in is of the order of the bias current of M₂. Thus, current amplifiers amplify currents of some microamperes. The dynamic range of a current amplifier can be improved considerably by using a symmetrical mirror instead of a simple mirror.

  A realistic circuit of a current amplifier based on a single current mirror is shown in Fig.9.

Fig.9  ACMOS current amplifier

Fig.10  Frequency responce of the amplifier in Fig.9

 The bandwidth of the amplifier is almost independent of the gain of the amplifier, (Fig.10). [5]

 

Spice input file of Current amplifier (Fig. 9)

Vdd 4 0 5 Vss 5 0 -5 Ii 0 1 ac 1 .model nm nmos level=1 VTO=0.85 KP=5e-5 + GAMMA=0.2 LAMBDA=0.02 PHI=0.6 + CGSO=4e-10 CGDO=4e-10 .model pm pmos level=1 VTO=-0.85 KP=23-5 + GAMMA=0.6 LAMBDA=0.05 PHI=0.6 + CGSO=4e-10 CGDO=4e-10 M1 13 1 11 5 nm w=30u l=5u M2 1 1 10 5 nm w=30u l=5u M3 11 12 5 5 nm w=30u l=5u M4 10 12 5 5 nm w=30u l=5u M5 4 1 12 5 nm w=30u l=5u M6 12 12 5 5 nm w=30u l=5u

M7 13 2 9 4 pm w=50u l=5u M8 1 2 7 4 pm w=50u l=5u M9 9 3 4 4 pm w=50u l=5u M10 7 3 4 4 pm w=50u l=5u M11 3 3 4 4 pm w=50u l=5u M12 8 3 4 4 pm w=50u l=5u M13 2 2 8 4 pm w=50u l=5u M14 5 2 3 4 pm w=50u l=5u RB 2 0 100k RL 13 0 1k .op .ac oct 10 10 1.000g  .print ac I(ii) I(RL) .end

 

A Current amplifier based on a symmetrical current mirror

  To improve the dynamic range of current amplifiers symmetrical cascode current mirrors are used, as it is shown in Fig.11. Properly designed, the input current can be much higher than the bias current. This amplifier can also be designed for low voltage low power operation.

Fig.11  Current amplifier based on symmetrical cascode current mirrors

(For k=1 , all PMOS are W/L=1.05, and all NMOS are W/L=0.47)

a)	b)

Fig.12  a) Transient response of the amplifier in Fig.11

  b) Transfer characteristic (I_bias =100nA, k=1)

The current amplification is defined by,