Chapter 5 Differential and Multistage Amplifier SJTU Zhou Lingling

Outline Introduction The CMOS Differential Pair Small-Signal Operation of the MOS Differential Pair The BJT Differential Pair The differential Amplifier with Active Load Frequency Response of the Differential amplifier Multistage Amplifiers SJTU Zhou Lingling

Introduction Two reasons of the differential amplifier suited for IC fabrication: IC fabrication is capable of providing matched devices. Utilizing more components than single-ended amplifier: Differential circuits are much less sensitive to noise and interference. Differential configuration enable us to bias the amplifier and to couple amplifier stages without the need for bypass and coupling capacitors. SJTU Zhou Lingling

The MOS Differential Pair Basic structure of differential pair. Characteristics SJTU Zhou Lingling

The MOS Differential Pair SJTU Zhou Lingling

Operation with a Common –Mode Input Voltage SJTU Zhou Lingling

Operation with a Common –Mode Input Voltage Symmetry circuit. Common-mode voltage. Current I divides equally between two transistors. The difference between two drains is zero. The differential pair rejects the common-mode input signals. SJTU Zhou Lingling

Operation with a Differential Input Voltage The MOS differential pair with a differential input signal vid applied. With vid positive: vGS1 > vGS2, iD1 > iD2, and vD1 < vD2; thus (vD2 - vD1) will be positive. With vid negative: vGS1 < vGS2, iD1 < iD2, and vD1 > vD2; thus (vD2 - vD1) will be negative. SJTU Zhou Lingling

Operation with a Differential Input Voltage Response to the differential input signal. The current I can be steered from one transistor to the other by varying the differential input voltage in the range: When differential input voltage is very small, the differential output voltage is proportional to it, and the gain is high. SJTU Zhou Lingling

Large-Signal Operation Transfer characteristic curves Normalized plots of the currents in a MOSFET differential pair. Note that VOV is the overdrive voltage at which Q1 and Q2 operate when conducting drain currents equal to I/2. SJTU Zhou Lingling

Large-Signal Operation Nonlinear curves. Maximum value of input differential voltage. When vid = 0, two drain currents are equal to I/2. Linear segment. Linearity can be increased by increasing overdrive voltage(see next slide). Price paid is a reduction in gain(current I is kept constant). SJTU Zhou Lingling

Large-Signal Operation The linear range of operation of the MOS differential pair can be extended by operating the transistor at a higher value of VOV. SJTU Zhou Lingling

Small-Signal Operation of MOS Differential Pair Linear amplifier Differential gain Common-mode gain Common-mode rejection ratio(CMRR) Mismatch on CMRR SJTU Zhou Lingling

Differential Gain a common-mode voltage applied to set the dc bias voltage at the gates. vid applied in a complementary (or balanced) manner. SJTU Zhou Lingling

Differential Gain Signal voltage at the joint source connection must be zero. SJTU Zhou Lingling

Differential Gain An alternative way of looking at the small-signal operation of the circuit. SJTU Zhou Lingling

Differential Gain Differential gain Output taken single-ended Output taken differentially Advantages of output signal taken differentially Reject common-mode signal Increase in gain by a factor of 2(6dB) SJTU Zhou Lingling

Differential Gain MOS differential amplifier with ro and RSS taken into account. SJTU Zhou Lingling

Differential Gain Equivalent circuit for determining the differential gain. Each of the two halves of the differential amplifier circuit is a common-source amplifier, known as its differential “half-circuit.” SJTU Zhou Lingling

Differential Gain Differential gain Output taken single-ended Output taken differentially SJTU Zhou Lingling

Common-Mode Gain The MOS differential amplifier with a common-mode input signal vicm. SJTU Zhou Lingling

Common-Mode Gain Equivalent circuit for determining the common-mode gain (with ro ignored). Each half of the circuit is known as the “common-mode half-circuit.” SJTU Zhou Lingling

Common-Mode Gain Common-mode gain Output taken single-ended Output taken differentially SJTU Zhou Lingling

Common-Mode Rejection Ratio Common-mode rejection ratio(CMRR) Output taken single-ended Output taken differentially This is true only when the circuit is perfectly matched. SJTU Zhou Lingling

Mismatch on CMRR Effect of RD mismatch on CMRR Effect of gm mismatch on CMRR SJTU Zhou Lingling

Mismatch on CMRR Determine the common-mode gain resulting from a mismatch in the gm values of Q1 and Q2. Common-mode half circuit is not available due to mismatch in circuit. The nominal value gm. SJTU Zhou Lingling

Mismatch on CMRR Effect of gm mismatch on CMRR SJTU Zhou Lingling

The BJT Differential Pair Basic operation Large-signal operation Small-signal operation Differential gain Common-mode gain Common-mode rejection ration SJTU Zhou Lingling

The BJT Differential Pair The basic BJT differential-pair configuration. SJTU Zhou Lingling

Basic Operation The differential pair with a common-mode input signal vCM. Two transistors are matched. Current source with infinite output resistance. Current I divide equally between two transistors. The difference in voltage between the two collector is zero. The differential pair rejects the common-mode input signal as long as two transistors remain in active region. SJTU Zhou Lingling

Basic Operation The differential pair with a “large” differential input signal. Q1 is on and Q2 is off. Current I entirely flows in Q1. SJTU Zhou Lingling

Basic Operation The differential pair with a large differential input signal of polarity opposite to that in (b). Q2 is on and Q1 is off. Current I entirely flows in Q2. SJTU Zhou Lingling

Basic Operation The differential pair with a small differential input signal vi. Small signal operation or linear amplifier. Assuming the bias current source I to be ideal and thus I remains constant with the change in vCM. Increment in Q1 and decrement in Q2. SJTU Zhou Lingling

Large-Signal Operation SJTU Zhou Lingling

Large-Signal Operation Nonlinear curves. Linear segments. Maximum value of input differential voltages Enlarge the linear segment by including equal resistance Re in series with the emitters. SJTU Zhou Lingling

Large-Signal Operation The transfer characteristics of the BJT differential pair (a) can be linearized by including resistances in the emitters. SJTU Zhou Lingling

Small Signal Operation The currents and voltages in the differential amplifier when a small differential input signal vid is applied. SJTU Zhou Lingling

Small Signal Operation A simple technique for determining the signal currents in a differential amplifier excited by a differential voltage signal vid; dc quantities are not shown. SJTU Zhou Lingling

Small Signal Operation A differential amplifier with emitter resistances. Only signal quantities are shown (in color). SJTU Zhou Lingling

Input Differential Resistance Input differential resistance is finite. The resistance seen between the two bases is equal to the total resistance in the emitter circuit multiplied by (1+β). Input differential resistance of differential pair with emitter resistors. SJTU Zhou Lingling

Differential Voltage Gain Output voltage taken single-ended Output voltage taken differentially SJTU Zhou Lingling

Differential Voltage Gain Differential voltage gain of the differential pair with resistances in the emitter leads Output voltage taken single-ended Output voltage taken differentially The voltage gain is equal to the ratio of the total resistance in the collector circuit to the total resistance in the emitter circuit. SJTU Zhou Lingling

Differential Half-Circuit Analysis Differential input signals. Single voltage at joint emitters is zero. The circuit is symmetric. Equivalent common-emitter amplifiers in (b). SJTU Zhou Lingling

Differential Half-Circuit Analysis This equivalence applies only for differential input signals. Either of the two common-emitter amplifiers can be used to find the differential gain, differential input resistance, frequency response, and so on, of the differential amplifier. Half circuit is biased at I/2. The voltage gain(with the output taken differentially) is equal to the voltage of half circuit. SJTU Zhou Lingling

Differential Half-Circuit Analysis The differential amplifier fed in a single-ended fashion. Signal voltage at the emitter is not zero. Almost identical to the symmetric one. SJTU Zhou Lingling

Common-Mode Gain The differential amplifier fed by a common-mode voltage signal vicm. SJTU Zhou Lingling

Common-Mode Gain Equivalent “half-circuits” for common-mode calculations. SJTU Zhou Lingling

Common-Mode Gain Common-mode voltage gain Output voltage taken single-ended Output voltage taken differentially SJTU Zhou Lingling

Common-Mode Rejection Ratio Output voltage taken single-ended Output voltage taken differentially This is true only when the circuit is symmetric. Mismatch on CMRR SJTU Zhou Lingling

Input Common-Mode Resistance Definition of the input common-mode resistance Ricm. The equivalent common-mode half-circuit. SJTU Zhou Lingling

Input Common-Mode Resistance Input common-mode resistance is very large. SJTU Zhou Lingling

Example SJTU Zhou Lingling

Example (cont’d) Evaluate the following: The input differential resistance. The overall differential voltage gain(neglect the effect of ro). The worst-case common-mode gain if the two collector resistance are accurate within ±1%. The CMRR, in dB. The input common-mode resistance(suppose the Early voltage is 100V). SJTU Zhou Lingling

The Differential Amplifier with Active Load Replace resistance RD with a constant current source results in a much high voltage gain as well as saving in chip area. Convert the output from differential to single-ended. SJTU Zhou Lingling

Differential-to-Single-Ended Conversion A simple but inefficient approach for differential to single-ended conversion. SJTU Zhou Lingling

The Active-Loaded MOS Differential Pair SJTU Zhou Lingling

The Active-Loaded MOS Differential Pair The circuit at equilibrium assuming perfect matching. SJTU Zhou Lingling

The Active-Loaded MOS Differential Pair The circuit with a differential input signal applied, neglecting the ro of all transistors. SJTU Zhou Lingling

Differential Gain of the Active-Loaded MOS Pair The output resistance ro plays a significant role in the operation of active-loaded amplifier. Asymmetric circuit. Half-circuit is not available. The gain will be determined as GmRo SJTU Zhou Lingling

Short-Circuit Transconductance Determining the short-circuit transconductance Gm = io/vid SJTU Zhou Lingling

Short-Circuit Transconductance SJTU Zhou Lingling

Output Resistance Circuit for determining Ro. The circled numbers indicate the order of the analysis steps. SJTU Zhou Lingling

Output Resistance Circuit for determining Ro. The circled numbers indicate the order of the analysis steps. SJTU Zhou Lingling

Differential Gain The differential gain is determined as GmRo When SJTU Zhou Lingling

Common-Mode Gain and CMRR Analysis of the active-loaded MOS differential amplifier to determine its common-mode gain. Power supplies eliminated. Rss is the output resistance of the current source. SJTU Zhou Lingling

Common-Mode Gain and CMRR Asymmetric circuit. Each of the two transistors as a CS configuration with a large source degeneration resistance 2Rss. Common-mode gain: CMRR SJTU Zhou Lingling

The Bipolar Differential Pair with Active Load Active-loaded bipolar differential pair. SJTU Zhou Lingling

Determine the Transconductance SJTU Zhou Lingling

Determine the output Resistance SJTU Zhou Lingling

Differential Gain The differential gain is determined as GmRo When Input differential resistance SJTU Zhou Lingling

Common-Mode Gain and CMRR SJTU Zhou Lingling

Frequency Response of the Resistively Loaded MOS Amplifier A resistively loaded MOS differential pair with the transistor supplying the bias current explicitly shown. It is assumed that the total impedance between node S and ground, ZSS, consists of a resistance RSS in parallel with a capacitance CSS. SJTU Zhou Lingling

Frequency Response of the Resistively Loaded MOS Amplifier (b) Differential half-circuit. (c) Common-mode half-circuit. SJTU Zhou Lingling

Frequency Response of the Resistively Loaded MOS Amplifier common-mode gain SJTU Zhou Lingling

Frequency Response of the Resistively Loaded MOS Amplifier Differential Gain SJTU Zhou Lingling

Frequency Response of the Resistively Loaded MOS Amplifier CMRR with frequency. SJTU Zhou Lingling

Multistage Amplifier A four-stage bipolar op amplifier A two-stage CMOS op amplifier SJTU Zhou Lingling

Multistage Amplifier SJTU Zhou Lingling

Multistage Amplifier The first stage(input stage) is differential-in, differential-out and consists of Q1 and Q2. The second stage is differential-in, single-ended-out amplifier which consists of Q3 and Q4. The third stage is CE amplifier which consists of pnp transistor Q7 to shifting the dc level. The last stage is the emitter follower. Biasing stage. SJTU Zhou Lingling

SJTU Zhou Lingling

Multistage Amplifier Equivalent circuit for calculating the gain of the input stage of the example. Input differential resistance Gain of first stage SJTU Zhou Lingling

Multistage Amplifier Equivalent circuit for calculating the gain of the second stage of the example. Gain of second stage SJTU Zhou Lingling

Multistage Amplifier Equivalent circuit for calculating the gain of the third stage of the example. Gain of third stage SJTU Zhou Lingling

Multistage Amplifier Equivalent circuit for calculating the gain of the output stage of the example. Gain of output stage Output resistance SJTU Zhou Lingling

Two-Stage CMOS Op-Amp Configuration SJTU Zhou Lingling